Temat: total-coloring - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: A note on total colorings of planar graphs without 4-cycles
Autorzy:: Wang, Ping
Wu, Jian-Liang
Powiązania:: https://bibliotekanauki.pl/articles/744436.pdf
Data publikacji:: 2004
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: total coloring
planar graph
list coloring
girth
Opis:: Let G be a 2-connected planar graph with maximum degree Δ such that G has no cycle of length from 4 to k, where k ≥ 4. Then the total chromatic number of G is Δ +1 if (Δ,k) ∈ {(7,4),(6,5),(5,7),(4,14)}.
Źródło:: Discussiones Mathematicae Graph Theory; 2004, 24, 1; 125-135
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Zmień widok

na półce

Skocz do pozycji: 2.

Tytuł:: Edge-choosability and total-choosability of planar graphs with no adjacent 3-cycles
Autorzy:: Cranston, Daniel
Powiązania:: https://bibliotekanauki.pl/articles/743133.pdf
Data publikacji:: 2009
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: list coloring
edge coloring
total coloring
Vizing's Conjecture
Opis:: Let G be a planar graph with no two 3-cycles sharing an edge. We show that if Δ(G) ≥ 9, then χ'ₗ(G) = Δ(G) and χ''ₗ(G) = Δ(G)+1. We also show that if Δ(G) ≥ 6, then χ'ₗ(G) ≤ Δ(G)+1 and if Δ(G) ≥ 7, then χ''ₗ(G) ≤ Δ(G)+2. All of these results extend to graphs in the projective plane and when Δ(G) ≥ 7 the results also extend to graphs in the torus and Klein bottle. This second edge-choosability result improves on work of Wang and Lih and of Zhang and Wu. All of our results use the discharging method to prove structural lemmas about the existence of subgraphs with small degree-sum. For example, we prove that if G is a planar graph with no two 3-cycles sharing an edge and with Δ(G) ≥ 7, then G has an edge uv with d(u) ≤ 4 and d(u)+d(v) ≤ Δ(G)+2. All of our proofs yield linear-time algorithms that produce the desired colorings.
Źródło:: Discussiones Mathematicae Graph Theory; 2009, 29, 1; 163-178
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Zmień widok

na półce

Skocz do pozycji: 3.

Tytuł:: Intersection graph of gamma sets in the total graph
Autorzy:: Chelvam, T.
Asir, T.
Powiązania:: https://bibliotekanauki.pl/articles/743214.pdf
Data publikacji:: 2012
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: total graph
gamma sets
intersection graph
Hamiltonian
coloring
connectivity
domination number
Opis:: In this paper, we consider the intersection graph $I_{Γ}(ℤₙ)$ of gamma sets in the total graph on ℤₙ. We characterize the values of n for which $I_{Γ}(ℤₙ)$ is complete, bipartite, cycle, chordal and planar. Further, we prove that $I_{Γ}(ℤₙ)$ is an Eulerian, Hamiltonian and as well as a pancyclic graph. Also we obtain the value of the independent number, the clique number, the chromatic number, the connectivity and some domination parameters of $I_{Γ}(ℤₙ)$.
Źródło:: Discussiones Mathematicae Graph Theory; 2012, 32, 2; 341-356
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Zmień widok

na półce

Skocz do pozycji: 4.

Tytuł:: Fractional ($ \mathcal{P} , \mathcal{Q} $)-Total List Colorings of Graphs
Autorzy:: Kemnitz, Arnfried
Mihók, Peter
Voigt, Margit
Powiązania:: https://bibliotekanauki.pl/articles/30146708.pdf
Data publikacji:: 2013-03-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: graph property
total coloring
(P,Q)-total coloring
fractional coloring
fractional (P,Q)-total chromatic number
circular coloring
circular (P,Q)-total chromatic number
list coloring
(P,Q)-total (a
b)-list colorings
Opis:: Let $ r, s \in \mathbb{N}$, $r \ge s$, and $ \mathcal{P} $ and $ \mathcal{Q} $ be two additive and hereditary graph properties. A $ (P,Q) $-total $(r, s)$-coloring of a graph $G = (V,E)$ is a coloring of the vertices and edges of $G$ by $s$-element subsets of $ \mathbb{Z}_r$ such that for each color $i$, $0 \le i \le r − 1$, the vertices colored by subsets containing $i$ induce a subgraph of $G$ with property $ \mathcal{P} $, the edges colored by subsets containing $i$ induce a subgraph of $G$ with property $ \mathcal{Q} $, and color sets of incident vertices and edges are disjoint. The fractional $ (\mathcal{P}, \mathcal{Q})$-total chromatic number $ \chi_{f,P,Q}^{''}(G)$ of $G$ is defined as the infimum of all ratios $r//s$ such that $G$ has a $ ( \mathcal{P}, \mathcal{Q})$-total $(r, s)$-coloring. A $ ( \mathcal{P}, \mathcal{Q} $-total independent set $ T = V_T \cup E_T \subseteq V \cup E$ is the union of a set $V_T$ of vertices and a set $E_T$ of edges of $G$ such that for the graphs induced by the sets $V_T$ and $E_T$ it holds that $ G[ V_T ] \in \mathcal{ P } $, $ G[ E_T ] \in \mathcal{Q} $, and $ G[ V_T ] $ and $ G[ E_T ] $ are disjoint. Let $ T_{ \mathcal{P} , \mathcal{Q} } $ be the set of all $ (\mathcal{P} ,\mathcal{Q})$-total independent sets of $G$. Let $L(x)$ be a set of admissible colors for every element $ x \in V \cup E $. The graph $G$ is called $ (\mathcal{P} , \mathcal{Q}) $-total $(a, b)$-list colorable if for each list assignment $L$ with $|L(x)| = a$ for all $x \in V \cup E$ it is possible to choose a subset $ C(x) \subseteq L(x)$ with $|C(x)| = b$ for all $ x \in V \cup E$ such that the set $ T_i $ which is defined by $ T_i = {x \in V \cup E : i \in C(x) } $ belongs to $ T_{ \mathcal{P},\mathcal{Q}}$ for every color $i$. The $ (\mathcal{P}, \mathcal{Q})$- choice ratio $ \text{chr}_{\mathcal{P},\mathcal{Q}}(G)$ of $G$ is defined as the infimum of all ratios $a//b$ such that $G$ is $ (\mathcal{P},\mathcal{Q})$-total $(a, b)$-list colorable. We give a direct proof of $ \chi_{ f,\mathcal{P},\mathcal{Q} }^{ \prime \prime } (G) = \text{chr}_{ \mathcal{P} ,\mathcal{Q} }(G)$ for all simple graphs $G$ and we present for some properties $ \mathcal{P} $ and $ \mathcal{Q} $ new bounds for the $ (\mathcal{P}, \mathcal{Q})$-total chromatic number and for the $(\mathcal{P},\mathcal{Q})$-choice ratio of a graph $G$.
Źródło:: Discussiones Mathematicae Graph Theory; 2013, 33, 1; 167-179
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Zmień widok

na półce

Skocz do pozycji: 5.

Tytuł:: Generalized Fractional Total Colorings of Complete Graph
Autorzy:: Karafová, Gabriela
Powiązania:: https://bibliotekanauki.pl/articles/30145422.pdf
Data publikacji:: 2013-09-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: fractional coloring
total coloring
complete graphs
Opis:: An additive and hereditary property of graphs is a class of simple graphs which is closed under unions, subgraphs and isomorphism. Let $P$ and $Q$ be two additive and hereditary graph properties and let $r,s$ be integers such that $r\geq s$. Then an $\frac{r}{s}$-fractional $(P,Q)$-total coloring of a finite graph $G=(V,E)$ is a mapping $f$, which assigns an $s$-element subset of the set $\{1,2,...,r\}$ to each vertex and each edge, moreover, for any color $i$ all vertices of color $i$ induce a subgraph of property $P$, all edges of color $i$ induce a subgraph of property $Q$ and vertices and incident edges have assigned disjoint sets of colors. The minimum ratio $\frac{r}{s}$ of an $\frac{r}{s}$-fractional $(P,Q)$-total coloring of $G$ is called fractional $(P,Q)$-total chromatic number $\chi_{f,P,Q}^{''}(G)=\frac{r}{s}$. Let $k=$ sup$\{i:K_{i+1}\in P\}$ and $l=$ sup$\{i:K_{i+1}\in Q\}$. We show for a complete graph $K_{n}$ that if $l\geq k+2$ then $\chi_{f,P,Q}^{''}(K_{n})=\frac{n}{k+1}$ for a sufficiently large $n$.
Źródło:: Discussiones Mathematicae Graph Theory; 2013, 33, 4; 665-676
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Zmień widok

na półce

Skocz do pozycji: 6.

Tytuł:: Vertex-Distinguishing IE-Total Colorings of Complete Bipartite Graphs K_m,N(m < n)
Autorzy:: Chen, Xiang’en
Gao, Yuping
Yao, Bing
Powiązania:: https://bibliotekanauki.pl/articles/30146641.pdf
Data publikacji:: 2013-05-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: complete bipartite graphs
IE-total coloring
vertex-distinguishing IE-total coloring
vertex-distinguishing IE-total chromatic number
Opis:: Let G be a simple graph. An IE-total coloring f of G is a coloring of the vertices and edges of G so that no two adjacent vertices receive the same color. Let C(u) be the set of colors of vertex u and edges incident to u under f. For an IE-total coloring f of G using k colors, if C(u) ≠ C(v) for any two different vertices u and v of G, then f is called a k-vertex-distinguishing IE-total-coloring of G, or a k-VDIET coloring of G for short. The minimum number of colors required for a VDIET coloring of G is denoted by χ_ie^vt(G), and is called vertex-distinguishing IE-total chromatic number or the VDIET chromatic number of G for short. VDIET colorings of complete bipartite graphs K_m,n(m < n) are discussed in this paper. Particularly, the VDIET chromatic numbers of K_m,n(1 ≤ m ≤ 7, m < n) as well as complete graphs K_n are obtained.
Źródło:: Discussiones Mathematicae Graph Theory; 2013, 33, 2; 289-306
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Zmień widok

na półce

Skocz do pozycji: 7.

Tytuł:: A Note on the Total Detection Numbers of Cycles
Autorzy:: Escuadro, Henry E.
Fujie, Futaba
Musick, Chad E.
Powiązania:: https://bibliotekanauki.pl/articles/31339492.pdf
Data publikacji:: 2015-05-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: vertex-distinguishing coloring
detectable labeling
detection number
total detection number
Hamiltonian graph
Opis:: Let G be a connected graph of size at least 2 and c :E(G)→{0, 1, . . ., k− 1} an edge coloring (or labeling) of G using k labels, where adjacent edges may be assigned the same label. For each vertex v of G, the color code of v with respect to c is the k-vector code(v) = (a₀, a₁, . . ., a_k−1), where ai is the number of edges incident with v that are labeled i for 0 ≤ i ≤ k − 1. The labeling c is called a detectable labeling if distinct vertices in G have distinct color codes. The value val(c) of a detectable labeling c of a graph G is the sum of the labels assigned to the edges in G. The total detection number td(G) of G is defined by td(G) = min{val(c)}, where the minimum is taken over all detectable labelings c of G. We investigate the problem of determining the total detection numbers of cycles.
Źródło:: Discussiones Mathematicae Graph Theory; 2015, 35, 2; 237-247
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Zmień widok

na półce

Skocz do pozycji: 8.

Tytuł:: Generalized Fractional and Circular Total Colorings of Graphs
Autorzy:: Kemnitz, Arnfried
Marangio, Massimiliano
Mihók, Peter
Oravcová, Janka
Soták, Roman
Powiązania:: https://bibliotekanauki.pl/articles/31339338.pdf
Data publikacji:: 2015-08-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: graph property
(P,Q)-total coloring
circular coloring
fractional coloring
fractional (P,Q)-total chromatic number
circular (P,Q)- total chromatic number
Opis:: Let $ \mathcal{P} $ and $ \mathcal{Q} $ be additive and hereditary graph properties, $ r, s \in \mathbb{N}$, $ r \ge s $, and $ [\mathbb{Z}_r]^s $ be the set of all s-element subsets of $\mathbb{Z}_r $. An ($r$, $s$)-fractional ($ \mathcal{P} $,$ \mathcal{Q} $)-total coloring of $G$ is an assignment $ h : V (G) \cup E(G) \rightarrow [\mathbb{Z}_r]^s $ such that for each $ i \in \mathbb{Z}_r $ the following holds: the vertices of $G$ whose color sets contain color $i$ induce a subgraph of $G$ with property $ \mathcal{P} $, edges with color sets containing color $i$ induce a subgraph of $G$ with property $ \mathcal{Q} $, and the color sets of incident vertices and edges are disjoint. If each vertex and edge of $G$ is colored with a set of $s$ consecutive elements of $ \mathbb{Z}_r $ we obtain an ($r$, $s$)-circular ($ \mathcal{P} $,$ \mathcal{Q} $)-total coloring of $G$. In this paper we present basic results on ($r$, $s$)-fractional/circular ($ \mathcal{P} $,$ \mathcal{Q} $)-total colorings. We introduce the fractional and circular ($ \mathcal{P} $,$ \mathcal{Q}$)-total chromatic number of a graph and we determine this number for complete graphs and some classes of additive and hereditary properties.
Źródło:: Discussiones Mathematicae Graph Theory; 2015, 35, 3; 517-532
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Zmień widok

na półce

Skocz do pozycji: 9.

Tytuł:: Generalized Fractional Total Colorings of Graphs
Autorzy:: Karafová, Gabriela
Soták, Roman
Powiązania:: https://bibliotekanauki.pl/articles/31339383.pdf
Data publikacji:: 2015-08-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: fractional coloring
total coloring
automorphism group
Opis:: Let $ \mathcal{P} $ and $ \mathcal{Q} $ be additive and hereditary graph properties and let $r$, $s$ be integers such that $ r \ge s $. Then an $ r/s$-fractional ($ \mathcal{P} $,$ \mathcal{Q} $)-total coloring of a finite graph $ G = (V, E) $ is a mapping $f$, which assigns an $s$-element subset of the set $ {1, 2, . . ., r}$ to each vertex and each edge, moreover, for any color $i$ all vertices of color $i$ induce a subgraph with property $ \mathcal{P} $, all edges of color $i$ induce a subgraph with property $ \mathcal{Q} $ and vertices and incident edges have been assigned disjoint sets of colors. The minimum ratio of an $ \frac{r}{s} $-fractional ($ \mathcal{P} $,$ \mathcal{Q} $)-total coloring of G is called fractional ($ \mathcal{P} $, $ \mathcal{Q} $)-total chromatic number $ \chi_{f, \mathcal{P} ,\mathcal{Q} }^{ \prime \prime } (G) = \frac{r}{s} $. We show in this paper that $ \chi_{f, \mathcal{P} ,\mathcal{Q} }^{ \prime \prime } $ of a graph $ G $ with $ o(V (G)) $ vertex orbits and $ o(E(G)) $ edge orbits can be found as a solution of a linear program with integer coefficients which consists only of $ o(V (G)) + o(E(G)) $ inequalities.
Źródło:: Discussiones Mathematicae Graph Theory; 2015, 35, 3; 463-473
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Zmień widok

na półce

Skocz do pozycji: 10.

Tytuł:: A Note on Neighbor Expanded Sum Distinguishing Index
Autorzy:: Flandrin, Evelyne
Li, Hao
Marczyk, Antoni
Saclé, Jean-François
Woźniak, Mariusz
Powiązania:: https://bibliotekanauki.pl/articles/31342189.pdf
Data publikacji:: 2017-02-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: general edge coloring
total coloring
neighbor-distinguishing index
neighbor sum distinguishing coloring
Opis:: A total k-coloring of a graph G is a coloring of vertices and edges of G using colors of the set [k] = {1, . . ., k}. These colors can be used to distinguish the vertices of G. There are many possibilities of such a distinction. In this paper, we consider the sum of colors on incident edges and adjacent vertices.
Źródło:: Discussiones Mathematicae Graph Theory; 2017, 37, 1; 29-37
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Zmień widok

na półce

Skocz do pozycji: 11.

Tytuł:: Cubic Graphs with Total Domatic Number at Least Two
Autorzy:: Akbari, Saieed
Motiei, Mohammad
Mozaffari, Sahand
Yazdanbod, Sina
Powiązania:: https://bibliotekanauki.pl/articles/31342441.pdf
Data publikacji:: 2018-02-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: total domination
total domatic number
coupon coloring
Opis:: Let G be a graph with no isolated vertex. A total dominating set of G is a set S of vertices of G such that every vertex is adjacent to at least one vertex in S. The total domatic number of a graph is the maximum number of total dominating sets which partition the vertex set of G. In this paper we provide a criterion under which a cubic graph has total domatic number at least two.
Źródło:: Discussiones Mathematicae Graph Theory; 2018, 38, 1; 75-82
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Zmień widok

na półce

Skocz do pozycji: 12.

Tytuł:: Rainbow Total-Coloring of Complementary Graphs and Erdős-Gallai Type Problem For The Rainbow Total-Connection Number
Autorzy:: Sun, Yuefang
Jin, Zemin
Tu, Jianhua
Powiązania:: https://bibliotekanauki.pl/articles/31342242.pdf
Data publikacji:: 2018-11-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: Rainbow total-coloring
rainbow total-connection number
complementary graph
Erdős-Gallai type problem
Opis:: A total-colored graph $G$ is rainbow total-connected if any two vertices of $G$ are connected by a path whose edges and internal vertices have distinct colors. The rainbow total-connection number, denoted by $ rtc(G) $, of a graph $G$ is the minimum number of colors needed to make $G$ rainbow total-connected. In this paper, we prove that $ rtc(G) $ can be bounded by a constant 7 if the following three cases are excluded: $ diam( \overline{G} ) = 2 $, $ diam( \overline{G} ) = 3 $, $ \overline{G} $ contains exactly two connected components and one of them is a trivial graph. An example is given to show that this bound is best possible. We also study Erdős-Gallai type problem for the rainbow total-connection number, and compute the lower bounds and precise values for the function $ f(n, k) $, where $ f(n, k) $ is the minimum value satisfying the following property: if $ |E(G)| \ge f(n, k) $, then $ rtc(G) \le k $.
Źródło:: Discussiones Mathematicae Graph Theory; 2018, 38, 4; 1023-1036
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Zmień widok

na półce

Skocz do pozycji: 13.

Tytuł:: Total Colorings of Embedded Graphs with No 3-Cycles Adjacent to 4-Cycles
Autorzy:: Wang, Bing
Wu, Jian-Liang
Sun, Lin
Powiązania:: https://bibliotekanauki.pl/articles/31342246.pdf
Data publikacji:: 2018-11-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: total coloring
embedded graph
cycle
Opis:: A total-k-coloring of a graph G is a coloring of V ∪ E using k colors such that no two adjacent or incident elements receive the same color. The total chromatic number χ′′(G) of G is the smallest integer k such that G has a total-k-coloring. Let G be a graph embedded in a surface of Euler characteristic ε ≥ 0. If G contains no 3-cycles adjacent to 4-cycles, that is, no 3-cycle has a common edge with a 4-cycle, then χ′′(G) ≤ max{8, Δ+1}.
Źródło:: Discussiones Mathematicae Graph Theory; 2018, 38, 4; 977-989
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Zmień widok

na półce

Skocz do pozycji: 14.

Tytuł:: Zig-zag facial total-coloring of plane graphs
Autorzy:: Czap, J.
Jendrol, S.
Voigt, M.
Powiązania:: https://bibliotekanauki.pl/articles/255827.pdf
Data publikacji:: 2018
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: plane graph
facial coloring total-coloring zig-zag coloring
Opis:: In this paper we introduce the concept of zig-zag facial total-coloring of plane graphs. We obtain lower and upper bounds for the minimum number of colors which is necessary for such a coloring. Moreover, we give several sharpness examples and formulate some open problems.
Źródło:: Opuscula Mathematica; 2018, 38, 6; 819-827
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Zmień widok

na półce

Skocz do pozycji: 15.

Tytuł:: Facial [r,s,t]-Colorings of Plane Graphs
Autorzy:: Czap, Július
Šugerek, Peter
Jendrol’, Stanislav
Valiska, Juraj
Powiązania:: https://bibliotekanauki.pl/articles/31343366.pdf
Data publikacji:: 2019-08-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: plane graph
boundary walk
edge-coloring
vertex-coloring
total-coloring
Opis:: Let $G$ be a plane graph. Two edges are facially adjacent in $G$ if they are consecutive edges on the boundary walk of a face of $G$. Given nonnegative integers $r$, $s$, and $t$, a facial $[r, s, t]$-coloring of a plane graph $G = (V,E)$ is a mapping $f : V \cup E \rightarrow {1, . . ., k} $ such that $ |f(v_1) − f(v_2)| \ge r $ for every two adjacent vertices $ v_1 $ and $ v_2 $, $ | f(e_1) − f(e_2)| \ge s $ for every two facially adjacent edges $ e_1 $ and $ e_2 $, and $ | f(v) − f(e)| \ge t $ for all pairs of incident vertices $ v $ and edges $ e $. The facial $[r, s, t]$-chromatic number $ \overline{ \chi }_{r,s,t} (G) $ of $ G $ is defined to be the minimum $k$ such that $G$ admits a facial $[r, s, t]$-coloring with colors $1, . . ., k$. In this paper we show that $ \overline{ \chi }_{r,s,t} (G) \le 3r + 3s + t + 1 $ for every plane graph $G$. For some triplets $ [r, s, t] $ and for some families of plane graphs this bound is improved. Special attention is devoted to the cases when the parameters $r$, $s$, and $t$ are small.
Źródło:: Discussiones Mathematicae Graph Theory; 2019, 39, 3; 629-645
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Zmień widok

na półce

Informacja

Wyszukujesz frazę "total-coloring" wg kryterium: Temat

Źródło danych

Dostawca treści

Kolekcja

Rok wydania

Wydawca

Temat

Autor

Typ dokumentu

Język