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Tytuł:
2-distance 4-colorability of planar subcubic graphs with girth at least 22
Autorzy:
Borodin, Oleg
Ivanova, Anna
Powiązania:
https://bibliotekanauki.pl/articles/743713.pdf
Data publikacji:
2012
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
planar graph
subcubic graph
2-distance coloring
Opis:
The trivial lower bound for the 2-distance chromatic number χ₂(G) of any graph G with maximum degree Δ is Δ+1. It is known that χ₂ = Δ+1 if the girth g of G is at least 7 and Δ is large enough. There are graphs with arbitrarily large Δ and g ≤ 6 having χ₂(G) ≥ Δ+2. We prove the 2-distance 4-colorability of planar subcubic graphs with g ≥ 22.
Źródło:
Discussiones Mathematicae Graph Theory; 2012, 32, 1; 141-151
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
2-Distance Colorings of Integer Distance Graphs
Autorzy:
Benmedjdoub, Brahim
Bouchemakh, Isma
Sopena, Éric
Powiązania:
https://bibliotekanauki.pl/articles/31343379.pdf
Data publikacji:
2019-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
2-distance coloring
integer distance graph
Opis:
A 2-distance k-coloring of a graph G is a mapping from V (G) to the set of colors {1,. . ., k} such that every two vertices at distance at most 2 receive distinct colors. The 2-distance chromatic number χ2(G) of G is then the smallest k for which G admits a 2-distance k-coloring. For any finite set of positive integers D = {d1, . . ., dℓ}, the integer distance graph G = G(D) is the infinite graph defined by V (G) = ℤ and uv ∈ E(G) if and only if |v − u| ∈ D. We study the 2-distance chromatic number of integer distance graphs for several types of sets D. In each case, we provide exact values or upper bounds on this parameter and characterize those graphs G(D) with χ2(G(D)) = ∆(G(D)) + 1.
Źródło:
Discussiones Mathematicae Graph Theory; 2019, 39, 2; 589-603
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
3-consecutive c-colorings of graphs
Autorzy:
Bujtás, Csilla
Sampathkumar, E.
Tuza, Zsolt
Subramanya, M.
Dominic, Charles
Powiązania:
https://bibliotekanauki.pl/articles/744032.pdf
Data publikacji:
2010
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
graph coloring
vertex coloring
consecutive coloring
upper chromatic number
Opis:
A 3-consecutive C-coloring of a graph G = (V,E) is a mapping φ:V → ℕ such that every path on three vertices has at most two colors. We prove general estimates on the maximum number $(χ̅)_{3CC}(G)$ of colors in a 3-consecutive C-coloring of G, and characterize the structure of connected graphs with $(χ̅)_{3CC}(G) ≥ k$ for k = 3 and k = 4.
Źródło:
Discussiones Mathematicae Graph Theory; 2010, 30, 3; 393-405
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A Note on Polynomial Algorithm for Cost Coloring of Bipartite Graphs with Δ ≤ 4
Autorzy:
Giaro, Krzysztof
Kubale, Marek
Powiązania:
https://bibliotekanauki.pl/articles/31526308.pdf
Data publikacji:
2020-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
bipartite graph
chromatic sum
cost coloring
NP-completeness
polynomial algorithm
Opis:
In the note we consider vertex coloring of a graph in which each color has an associated cost which is incurred each time the color is assigned to a vertex. The cost of coloring is the sum of costs incurred at each vertex. We show that the minimum cost coloring problem for n-vertex bipartite graph of degree Δ ≤ 4 can be solved in O(n2) time. This extends Jansen’s result [K. Jansen, The optimum cost chromatic partition problem, in: Proc. CIAC’97, Lecture Notes in Comput. Sci. 1203 (1997) 25–36] for paths and cycles to subgraphs of biquartic graphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2020, 40, 3; 885-891
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A Note on the Equitable Choosability of Complete Bipartite Graphs
Autorzy:
Mudrock, Jeffrey A.
Chase, Madelynn
Thornburgh, Ezekiel
Kadera, Isaac
Wagstrom, Tim
Powiązania:
https://bibliotekanauki.pl/articles/32325306.pdf
Data publikacji:
2021-11-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
graph coloring
equitable coloring
list coloring
equitable choos-ability
Opis:
In 2003 Kostochka, Pelsmajer, and West introduced a list analogue of equitable coloring called equitable choosability. A k-assignment, L, for a graph G assigns a list, L(v), of k available colors to each v ∈ V (G), and an equitable L-coloring of G is a proper coloring, f, of G such that f(v) ∈ L(v) for each v ∈ V (G) and each color class of f has size at most ⌈|V (G)|/k⌉. Graph G is said to be equitably k-choosable if an equitable L-coloring of G exists whenever L is a k-assignment for G. In this note we study the equitable choosability of complete bipartite graphs. A result of Kostochka, Pelsmajer, and West implies Kn,m is equitably k-choosable if k ≥ max{n, m} provided Kn,m ≠ K2l+1,2l+1. We prove Kn,m is equitably k-choosable if m ≤ ⌈ (m + n)/k⌉ (k − n) which gives Kn,m is equitably k-choosable for certain k satisfying k < max{n, m}. We also give a complete characterization of the equitable choosability of complete bipartite graphs that have a partite set of size at most 2.
Źródło:
Discussiones Mathematicae Graph Theory; 2021, 41, 4; 1091-1101
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
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, . . ., ak−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
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
Tytuł:
A note on vertex colorings of plane graphs
Autorzy:
Fabrici, Igor
Jendrol’, Stanislav
Soták, Roman
Powiązania:
https://bibliotekanauki.pl/articles/30148722.pdf
Data publikacji:
2014-11-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
plane graph
vertex coloring
Opis:
Given an integer valued weighting of all elements of a 2-connected plane graph G with vertex set V, let c(v) denote the sum of the weight of v ∈ V and of the weights of all edges and all faces incident with v. This vertex coloring of G is proper provided that c(u) ≠ c(v) for any two adjacent vertices u and v of G. We show that for every 2-connected plane graph there is such a proper vertex coloring with weights in {1, 2, 3}. In a special case, the value 3 is improved to 2.
Źródło:
Discussiones Mathematicae Graph Theory; 2014, 34, 4; 849-855
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A Survey on Packing Colorings
Autorzy:
Brešar, Boštjan
Ferme, Jasmina
Klavžar, Sandi
Rall, Douglas F.
Powiązania:
https://bibliotekanauki.pl/articles/31804166.pdf
Data publikacji:
2020-11-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
packing coloring
packing chromatic number
subcubic graph
S -packing chromatic number
computational complexity
Opis:
If S = (a1, a2, . . .) is a non-decreasing sequence of positive integers, then an S-packing coloring of a graph G is a partition of V (G) into sets X1, X2, . . . such that for each pair of distinct vertices in the set Xi, the distance between them is larger than ai. If there exists an integer k such that V (G) = X1 ∪ ∪ Xk, then the partition is called an S-packing k-coloring. The S-packing chromatic number of G is the smallest k such that G admits an S-packing k-coloring. If ai = i for every i, then the terminology reduces to packing colorings and packing chromatic number. Since the introduction of these generalizations of the chromatic number in 2008 more than fifty papers followed. Here we survey the state of the art on the packing coloring, and its generalization, the S-packing coloring. We also list several conjectures and open problems.
Źródło:
Discussiones Mathematicae Graph Theory; 2020, 40, 4; 923-970
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A Survey on the Cyclic Coloring and its Relaxations
Autorzy:
Czap, Július
Horňák, Mirko
Jendroľ, Stanislav
Powiązania:
https://bibliotekanauki.pl/articles/32083738.pdf
Data publikacji:
2021-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
plane graph
edge coloring
vertex coloring
Opis:
A cyclic coloring of a plane graph is a vertex coloring such that any two vertices incident with the same face receive distinct colors. This type of coloring was introduced more than fifty years ago, and a lot of research in chromatic graph theory was sparked by it. This paper is a survey on the state of the art concerning the cyclic coloring and relaxations of this graph invariant.
Źródło:
Discussiones Mathematicae Graph Theory; 2021, 41, 1; 5-38
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Adjacent vertex distinguishing edge-colorings of planar graphs with girth at least six
Autorzy:
Bu, Yuehua
Lih, Ko-Wei
Wang, Weifan
Powiązania:
https://bibliotekanauki.pl/articles/743930.pdf
Data publikacji:
2011
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
edge-coloring
vertex-distinguishing
planar graph
Opis:
An adjacent vertex distinguishing edge-coloring of a graph G is a proper edge-coloring o G such that any pair of adjacent vertices are incident to distinct sets of colors. The minimum number of colors required for an adjacent vertex distinguishing edge-coloring of G is denoted by χ'ₐ(G). We prove that χ'ₐ(G) is at most the maximum degree plus 2 if G is a planar graph without isolated edges whose girth is at least 6. This gives new evidence to a conjecture proposed in [Z. Zhang, L. Liu, and J. Wang, Adjacent strong edge coloring of graphs, Appl. Math. Lett., 15 (2002) 623-626.]
Źródło:
Discussiones Mathematicae Graph Theory; 2011, 31, 3; 429-439
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Analogues of cliques for oriented coloring
Autorzy:
Klostermeyer, William
MacGillivray, Gary
Powiązania:
https://bibliotekanauki.pl/articles/744524.pdf
Data publikacji:
2004
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
graph coloring
oriented coloring
clique
planar graph
Opis:
We examine subgraphs of oriented graphs in the context of oriented coloring that are analogous to cliques in traditional vertex coloring. Bounds on the sizes of these subgraphs are given for planar, outerplanar, and series-parallel graphs. In particular, the main result of the paper is that a planar graph cannot contain an induced subgraph D with more than 36 vertices such that each pair of vertices in D are joined by a directed path of length at most two.
Źródło:
Discussiones Mathematicae Graph Theory; 2004, 24, 3; 373-387
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Analysis of the efficiency of graph coloring algorithms
Autorzy:
Kubale, Marek
Powiązania:
https://bibliotekanauki.pl/articles/748571.pdf
Data publikacji:
1982
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Computational complexity and efficiency of algorithms
Coloring of graphs and hypergraphs
Graph theory
Opis:
.
This paper discusses the computational efficiency and the number of colors used by the following algorithms for coloring vertices of graphs: sequential coloring and sequential coloring with interchange algorithms for a largest-first and a smallest-last orderings of vertices, the coloring-pairs algorithm, and the approximately maximum independent set algorithm. Each algorithm is supplied with a Pascal-like program, time complexity in terms of the size of a graph, and worst-case behaviour. In conclusion, some computational results are included with support the estimations and suggest the sequential coloring with interchange algorithm for a largest-first vertex ordering as a method which uses the least number of colors for uniformly distributed random graphs.
Źródło:
Mathematica Applicanda; 1982, 10, 19
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Associative graph products and their independence, domination and coloring numbers
Autorzy:
Nowakowski, Richard
Rall, Douglas
Powiązania:
https://bibliotekanauki.pl/articles/972041.pdf
Data publikacji:
1996
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
graph products
independence
domination
irredundance
coloring
Opis:
Associative products are defined using a scheme of Imrich & Izbicki [18]. These include the Cartesian, categorical, strong and lexicographic products, as well as others. We examine which product ⊗ and parameter p pairs are multiplicative, that is, p(G⊗H) ≥ p(G)p(H) for all graphs G and H or p(G⊗H) ≤ p(G)p(H) for all graphs G and H. The parameters are related to independence, domination and irredundance. This includes Vizing's conjecture directly, and indirectly the Shannon capacity of a graph and Hedetniemi's coloring conjecture.
Źródło:
Discussiones Mathematicae Graph Theory; 1996, 16, 1; 53-79
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Backbone colorings along stars and matchings in split graphs: their span is close to the chromatic number
Autorzy:
Broersma, Hajo
Marchal, Bert
Paulusma, Daniel
Salman, A.
Powiązania:
https://bibliotekanauki.pl/articles/743123.pdf
Data publikacji:
2009
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
backbone coloring
split graph
matching
star
Opis:
We continue the study on backbone colorings, a variation on classical vertex colorings that was introduced at WG2003. Given a graph G = (V,E) and a spanning subgraph H of G (the backbone of G), a λ-backbone coloring for G and H is a proper vertex coloring V→ {1,2,...} of G in which the colors assigned to adjacent vertices in H differ by at least λ. The algorithmic and combinatorial properties of backbone colorings have been studied for various types of backbones in a number of papers. The main outcome of earlier studies is that the minimum number l of colors, for which such colorings V→ {1,2,...,l} exist, in the worst case is a factor times the chromatic number (for path, tree, matching and star backbones). We show here that for split graphs and matching or star backbones, l is at most a small additive constant (depending on λ) higher than the chromatic number. Our proofs combine algorithmic and combinatorial arguments. We also indicate other graph classes for which our results imply better upper bounds on l than the previously known bounds.
Źródło:
Discussiones Mathematicae Graph Theory; 2009, 29, 1; 143-162
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 95

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