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Tytuł:
On arc-coloring of digraphs
Autorzy:
Zwonek, M.
Powiązania:
https://bibliotekanauki.pl/articles/254973.pdf
Data publikacji:
2006
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
arc-coloring
digraph
Opis:
In the paper we deal with the problem of the arc-colouring of some classes of digraphs (tournaments, complete digraphs and products of digraphs).
Źródło:
Opuscula Mathematica; 2006, 26, 1; 185-195
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
New models and algorithms for RNA pseudoknot order assignment
Autorzy:
Zok, Tomasz
Badura, Jan
Swat, Sylwester
Figurski, Kacper
Popenda, Mariusz
Antczak, Maciej
Powiązania:
https://bibliotekanauki.pl/articles/911230.pdf
Data publikacji:
2020
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
RNA pseudoknot order
conflict graph
vertex coloring
maximum independent set
integer programming
kolorowanie grafu
zbiór niezależny
programowanie całkowitoliczbowe
Opis:
The pseudoknot is a specific motif of the RNA structure that highly influences the overall shape and stability of a molecule. It occurs when nucleotides of two disjoint single-stranded fragments of the same chain, separated by a helical fragment, interact with each other and form base pairs. Pseudoknots are characterized by great topological diversity, and their systematic description is still a challenge. In our previous work, we have introduced the pseudoknot order: a new coefficient representing the topological complexity of the pseudoknotted RNA structure. It is defined as the minimum number of base pair set decompositions, aimed to obtain the unknotted RNA structure. We have suggested how it can be useful in the interpretation and understanding of a hierarchy of RNA folding. However, it is not trivial to unambiguously identify pseudoknots and determine their orders in an RNA structure. Therefore, since the introduction of this coefficient, we have worked on the method to reliably assign pseudoknot orders in correspondence to the mechanisms that control the biological process leading to their formation in the molecule. Here, we introduce a novel graph coloring-based model for the problem of pseudoknot order assignment. We show a specialized heuristic operating on the proposed model and an alternative integer programming algorithm. The performance of both approaches is compared with that of state-of-the-art algorithms which so far have been most efficient in solving the problem in question. We summarize the results of computational experiments that evaluate our new methods in terms of classification quality on a representative data set originating from the non-redundant RNA 3D structure repository.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2020, 30, 2; 315-324
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the Star Chromatic Index of Generalized Petersen Graphs
Autorzy:
Zhu, Enqiang
Shao, Zehui
Powiązania:
https://bibliotekanauki.pl/articles/32083878.pdf
Data publikacji:
2021-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
star edge-coloring
star chromatic index
generalized Petersen graph
Opis:
The star $k$-edge-coloring of graph $G$ is a proper edge coloring using $k$ colors such that no path or cycle of length four is bichromatic. The minimum number $k$ for which $G$ admits a star $k$-edge-coloring is called the star chromatic index of $G$, denoted by $χ_s^′(G)$. Let $GCD(n, k)$ be the greatest common divisor of $n$ and $k$. In this paper, we give a necessary and sufficient condition of $χ_s^′(P(n, k)) = 4$ for a generalized Petersen graph $P(n, k)$ and show that “almost all” generalized Petersen graphs have a star 5-edge-colorings. Furthermore, for any two integers $k$ and $n(≥2k + 1)$ such that $GCD(n, k) ≥ 3, P (n, k)$ has a star 5-edge-coloring, with the exception of the case that $GCD(n, k) = 3$, $k ≠ GCD(n, k)$ and \(\frac{n}{3}≡1(mod3)\).
Źródło:
Discussiones Mathematicae Graph Theory; 2021, 41, 2; 427-439
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On choosability of complete multipartite graphs $K_{4,3*t,2*(k-2t-2),1*(t+1)}$
Autorzy:
Zheng, Guo-Ping
Shen, Yu-Fa
Chen, Zuo-Li
Lv, Jin-Feng
Powiązania:
https://bibliotekanauki.pl/articles/744583.pdf
Data publikacji:
2010
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
list coloring
complete multipartite graphs
chromatic-choosable graphs
Ohba's conjecture
Opis:
A graph G is said to be chromatic-choosable if ch(G) = χ(G). Ohba has conjectured that every graph G with 2χ(G)+1 or fewer vertices is chromatic-choosable. It is clear that Ohba's conjecture is true if and only if it is true for complete multipartite graphs. In this paper we show that Ohba's conjecture is true for complete multipartite graphs $K_{4,3*t,2*(k-2t-2),1*(t+1)}$ for all integers t ≥ 1 and k ≥ 2t+2, that is, $ch(K_{4,3*t,2*(k-2t-2),1*(t+1)}) = k$, which extends the results $ch(K_{4,3,2*(k-4),1*2}) = k$ given by Shen et al. (Discrete Math. 308 (2008) 136-143), and $ch(K_{4,3*2,2*(k-6),1*3}) = k$ given by He et al. (Discrete Math. 308 (2008) 5871-5877).
Źródło:
Discussiones Mathematicae Graph Theory; 2010, 30, 2; 237-244
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The use of Eulers formula in (3,1)*-list coloring
Autorzy:
Zhao, Yongqiang
He, Wenjie
Powiązania:
https://bibliotekanauki.pl/articles/743889.pdf
Data publikacji:
2006
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
list improper coloring
(L,d)*-coloring
(m,d)*-choosable
Euler's formula
Opis:
A graph G is called (k,d)*-choosable if, for every list assignment L satisfying |L(v)| = k for all v ∈ V(G), there is an L-coloring of G such that each vertex of G has at most d neighbors colored with the same color as itself. Ko-Wei Lih et al. used the way of discharging to prove that every planar graph without 4-cycles and i-cycles for some i ∈ {5,6,7} is (3,1)*-choosable. In this paper, we show that if G is 2-connected, we may just use Euler's formula and the graph's structural properties to prove these results. Furthermore, for 2-connected planar graph G, we use the same way to prove that, if G has no 4-cycles, and the number of 5-cycles contained in G is at most $11 + ⎣∑_{i≥5} [(5i-24)/4] |V_i|⎦$, then G is (3,1)*-choosable; if G has no 5-cycles, and any planar embedding of G does not contain any adjacent 3-faces and adjacent 4-faces, then G is (3,1)*-choosable.
Źródło:
Discussiones Mathematicae Graph Theory; 2006, 26, 1; 91-101
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On characterization of uniquely 3-list colorable complete multipartite graphs
Autorzy:
Zhao, Yancai
Shan, Erfang
Powiązania:
https://bibliotekanauki.pl/articles/744543.pdf
Data publikacji:
2010
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
list coloring
complete multipartite graph
uniquely 3-list colorable graph
Opis:
For each vertex v of a graph G, if there exists a list of k colors, L(v), such that there is a unique proper coloring for G from this collection of lists, then G is called a uniquely k-list colorable graph. Ghebleh and Mahmoodian characterized uniquely 3-list colorable complete multipartite graphs except for nine graphs: $K_{2,2,r}$ r ∈ {4,5,6,7,8}, $K_{2,3,4}$, $K_{1*4,4}$, $K_{1*4,5}$, $K_{1*5,4}$. Also, they conjectured that the nine graphs are not U3LC graphs. After that, except for $K_{2,2,r}$ r ∈ {4,5,6,7,8}, the others have been proved not to be U3LC graphs. In this paper we first prove that $K_{2,2,8}$ is not U3LC graph, and thus as a direct corollary, $K_{2,2,r}$ (r = 4,5,6,7,8) are not U3LC graphs, and then the uniquely 3-list colorable complete multipartite graphs are characterized completely.
Źródło:
Discussiones Mathematicae Graph Theory; 2010, 30, 1; 105-114
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Neighbor Sum Distinguishing Total Chromatic Number of Planar Graphs without 5-Cycles
Autorzy:
Zhao, Xue
Xu, Chang-Qing
Powiązania:
https://bibliotekanauki.pl/articles/32083807.pdf
Data publikacji:
2020-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
neighbor sum distinguishing total coloring
discharging method
planar graph
Opis:
For a given graph $ G = (V (G), E(G)) $, a proper total coloring $ \phi : V (G) \cup E(G) $ $ \rightarrow {1, 2, . . ., k} $ is neighbor sum distinguishing if $ f(u) \ne f(v) $ for each edge $ uv \in E(G) $, where $ f(v) = \Sigma_{ uv \in E(G) } $ $ \phi (uv) + \phi (v) $, $ v \in V (G) $. The smallest integer $k$ in such a coloring of $G$ is the neighbor sum distinguishing total chromatic number, denoted by $ \chi_\Sigma^{''} (G) $. Pilśniak and Woźniak first introduced this coloring and conjectured that $ \chi_\Sigma^{''}(G) \le \Delta (G)+3 $ for any graph with maximum degree $ \Delta (G) $. In this paper, by using the discharging method, we prove that for any planar graph $G$ without 5-cycles, $ \chi_\Sigma^{''} (G) \le \text{max} \{ \Delta (G)+2, 10 \} $. The bound $ \Delta (G) + 2 $ is sharp. Furthermore, we get the exact value of $ \chi_\Sigma^{''} (G) $ if $ \Delta (G) \ge 9 $.
Źródło:
Discussiones Mathematicae Graph Theory; 2020, 40, 1; 243-253
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Defective choosability of graphs in surfaces
Autorzy:
Woodall, Douglas
Powiązania:
https://bibliotekanauki.pl/articles/743943.pdf
Data publikacji:
2011
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
list coloring
defective coloring
minor-free graph
Opis:
It is known that if G is a graph that can be drawn without edges crossing in a surface with Euler characteristic ε, and k and d are positive integers such that k ≥ 3 and d is sufficiently large in terms of k and ε, then G is (k,d)*-colorable; that is, the vertices of G can be colored with k colors so that each vertex has at most d neighbors with the same color as itself. In this paper, the known lower bound on d that suffices for this is reduced, and an analogous result is proved for list colorings (choosability). Also, the recent result of Cushing and Kierstead, that every planar graph is (4,1)*-choosable, is extended to $K_{3,3}$-minor-free and K₅-minor-free graphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2011, 31, 3; 441-459
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Antipodal Edge-Colorings of Hypercubes
Autorzy:
West, Douglas B.
Wise, Jennifer I.
Powiązania:
https://bibliotekanauki.pl/articles/31343560.pdf
Data publikacji:
2019-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
antipodal edge-coloring
hypercube
monochromatic geodesic
Opis:
Two vertices of the k-dimensional hypercube Qk are antipodal if they differ in every coordinate. Edges uv and xy are antipodal if u is antipodal to x and v is antipodal to y. An antipodal edge-coloring of Qk is a 2- edge-coloring such that antipodal edges always have different colors. Norine conjectured that for k ≥ 2, in every antipodal edge-coloring of Qk some two antipodal vertices are connected by a monochromatic path. Feder and Subi proved this for k ≤ 5. We prove it for k ≤ 6.
Źródło:
Discussiones Mathematicae Graph Theory; 2019, 39, 1; 271-284
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:
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
Tytuł:
An Improved Upper Bound on Neighbor Expanded Sum Distinguishing Index
Autorzy:
Vučković, Bojan
Powiązania:
https://bibliotekanauki.pl/articles/32083737.pdf
Data publikacji:
2020-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
general edge coloring
total coloring
neighbor sum distinguishing index
Opis:
A total k-weighting f of a graph G is an assignment of integers from the set {1, . . ., k} to the vertices and edges of G. We say that f is neighbor expanded sum distinguishing, or NESD for short, if Σw∈N(v) (f(vw) + f(w)) differs from Σw∈N(u)(f(uw) + f(w)) for every two adjacent vertices v and u of G. The neighbor expanded sum distinguishing index of G, denoted by egndiΣ(G), is the minimum positive integer k for which there exists an NESD weighting of G. An NESD weighting was introduced and investigated by Flandrin et al. (2017), where they conjectured that egndiΣ(G) ≤ 2 for any graph G. They examined some special classes of graphs, while proving that egndiΣ(G) ≤ χ(G) + 1. We improve this bound and show that egndiΣ(G) ≤ 3 for any graph G. We also show that the conjecture holds for all bipartite, 3-regular and 4-regular graphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2020, 40, 1; 323-329
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
List coloring of complete multipartite graphs
Autorzy:
Vetrík, Tomáš
Powiązania:
https://bibliotekanauki.pl/articles/743641.pdf
Data publikacji:
2012
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
list coloring
choice number
complete multipartite graph
Opis:
The choice number of a graph G is the smallest integer k such that for every assignment of a list L(v) of k colors to each vertex v of G, there is a proper coloring of G that assigns to each vertex v a color from L(v). We present upper and lower bounds on the choice number of complete multipartite graphs with partite classes of equal sizes and complete r-partite graphs with r-1 partite classes of order two.
Źródło:
Discussiones Mathematicae Graph Theory; 2012, 32, 1; 31-37
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On Ramsey $(K_{1,2},C₄)$-minimal graphs
Autorzy:
Vetrík, Tomás
Yulianti, Lyra
Baskoro, Edy
Powiązania:
https://bibliotekanauki.pl/articles/744084.pdf
Data publikacji:
2010
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Ramsey-minimal graph
edge coloring
diameter of a graph
Opis:
For graphs F, G and H, we write F → (G,H) to mean that any red-blue coloring of the edges of F contains a red copy of G or a blue copy of H. The graph F is Ramsey (G,H)-minimal if F → (G,H) but F* ↛ (G,H) for any proper subgraph F* ⊂ F. We present an infinite family of Ramsey $(K_{1,2},C₄)$-minimal graphs of any diameter ≥ 4.
Źródło:
Discussiones Mathematicae Graph Theory; 2010, 30, 4; 637-649
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Choice-Perfect Graphs
Autorzy:
Tuza, Zsolt
Powiązania:
https://bibliotekanauki.pl/articles/30146654.pdf
Data publikacji:
2013-03-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
graph coloring
list coloring
choice-perfect graph
Opis:
Given a graph $ G = (V,E) $ and a set $ L_v $ of admissible colors for each vertex $ v \in V $ (termed the list at $v$), a list coloring of $G$ is a (proper) vertex coloring $ \phi : V \rightarrow \bigcup \text{}_{v \in V} L_v $ such that $ \phi (v) \in L_v $ for all $ v \in V $ and $ \phi(u) \ne \phi(v) $ for all $ uv \in E $. If such a $ \phi $ exists, $G$ is said to be list colorable. The choice number of $G$ is the smallest natural number $k$ for which $G$ is list colorable whenever each list contains at least $k$ colors. In this note we initiate the study of graphs in which the choice number equals the clique number or the chromatic number in every induced subgraph. We call them choice-ω-perfect and choice-χ-perfect graphs, respectively. The main result of the paper states that the square of every cycle is choice-χ-perfect.
Źródło:
Discussiones Mathematicae Graph Theory; 2013, 33, 1; 231-242
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 198

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