共查询到20条相似文献,搜索用时 46 毫秒
1.
Yoshihiro Asayama Yuki Kawasaki Seog-Jin Kim Atsuhiro Nakamoto Kenta Ozeki 《Discrete Mathematics》2018,341(11):2988-2994
An -dynamic -coloring of a graph is a proper -coloring such that any vertex has at least distinct colors in . The -dynamic chromatic number of a graph is the least such that there exists an -dynamic -coloring of .Loeb et al. (2018) showed that if is a planar graph, then , and there is a planar graph with . Thus, finding an optimal upper bound on for a planar graph is a natural interesting problem. In this paper, we show that if is a planar triangulation. The upper bound is sharp. 相似文献
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A star edge-coloring of a graph is a proper edge coloring such that every 2-colored connected subgraph of is a path of length at most 3. For a graph , let the list star chromatic index of , , be the minimum such that for any -uniform list assignment for the set of edges, has a star edge-coloring from . Dvo?ák et al. (2013) asked whether the list star chromatic index of every subcubic graph is at most 7. In Kerdjoudj et al. (2017) we proved that it is at most 8. In this paper we consider graphs with any maximum degree, we proved that if the maximum average degree of a graph is less than (resp. 3), then (resp. ). 相似文献
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Bojan Vučković 《Discrete Mathematics》2018,341(5):1472-1478
An adjacent vertex distinguishing total -coloring of a graph is a proper total -coloring of such that any pair of adjacent vertices have different sets of colors. The minimum number needed for such a total coloring of is denoted by . In this paper we prove that if , and in general. This improves a result in Huang et al. (2012) which states that for any graph with . 相似文献
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The neighbor-distinguishing total chromatic number of a graph is the smallest integer such that can be totally colored using colors with a condition that any two adjacent vertices have different sets of colors. In this paper, we give a sufficient and necessary condition for a planar graph with maximum degree 13 to have or . Precisely, we show that if is a planar graph of maximum degree 13, then ; and if and only if contains two adjacent 13-vertices. 相似文献
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Bojan Vučković 《Discrete Mathematics》2017,340(12):3092-3096
A proper edge coloring is neighbor-distinguishing if any two adjacent vertices have distinct sets consisting of colors of their incident edges. The minimum number of colors needed for a neighbor-distinguishing edge coloring is the neighbor-distinguishing index, denoted by . A graph is normal if it contains no isolated edges. Let be a normal graph, and let and denote the maximum degree and the chromatic index of , respectively. We modify the previously known techniques of edge-partitioning to prove that , which implies that . This improves the result in Wang et al. (2015), which states that for any normal graph. We also prove that when , is an integer with . 相似文献
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Jakub Przybyło 《Discrete Mathematics》2017,340(10):2402-2407
Consider a positive integer and a graph with maximum degree and without isolated edges. The least so that a proper edge colouring exists such that for every pair of distinct vertices at distance at most in is denoted by . For , it has been proved that . For any in turn an infinite family of graphs is known with . We prove that, on the other hand, for . In particular, we show that if . 相似文献
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For integers , a -coloring of a graph is a proper coloring with at most colors such that for any vertex with degree , there are at least min different colors present at the neighborhood of . The -hued chromatic number of , , is the least integer such that a -coloring of exists. The list-hued chromatic number of is similarly defined. Thus if , then . We present examples to show that, for any sufficiently large integer , there exist graphs with maximum average degree less than 3 that cannot be -colored. We prove that, for any fraction , there exists an integer such that for each , every graph with maximum average degree is list -colorable. We present examples to show that for some there exist graphs with maximum average degree less than 4 that cannot be -hued colored with less than colors. We prove that, for any sufficiently small real number , there exists an integer such that every graph with maximum average degree satisfies . These results extend former results in Bonamy et al. (2014). 相似文献
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A 2-coloring is a coloring of vertices of a graph with colors 1 and 2. Define for and We say that is -colorable if has a 2-coloring such that is an empty set or the induced subgraph has the maximum degree at most for and Let be a planar graph without 4-cycles and 5-cycles. We show that the problem to determine whether is -colorable is NP-complete for every positive integer Moreover, we construct non--colorable planar graphs without 4-cycles and 5-cycles for every positive integer In contrast, we prove that is -colorable where and 相似文献
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For a subgraph of , let be the maximum number of vertices of that are pairwise distance at least three in . In this paper, we prove three theorems. Let be a positive integer, and let be a subgraph of an -connected claw-free graph . We prove that if , then either can be covered by a cycle in , or there exists a cycle in such that . This result generalizes the result of Broersma and Lu that has a cycle covering all the vertices of if . We also prove that if , then either can be covered by a path in , or there exists a path in such that . By using the second result, we prove the third result. For a tree , a vertex of with degree one is called a leaf of . For an integer , a tree which has at most leaves is called a -ended tree. We prove that if , then has a -ended tree covering all the vertices of . This result gives a positive answer to the conjecture proposed by Kano et al. (2012). 相似文献
10.
We say a graph is -colorable with of ’s and of ’s if may be partitioned into independent sets and sets whose induced graphs have maximum degree at most . The maximum average degree, , of a graph is the maximum average degree over all subgraphs of . In this note, for nonnegative integers , we show that if , then is -colorable. 相似文献
11.
Carl Johan Casselgren Hrant H. Khachatrian Petros A. Petrosyan 《Discrete Mathematics》2018,341(3):627-637
An interval-coloring of a multigraph is a proper edge coloring with colors such that the colors of the edges incident with every vertex of are colored by consecutive colors. A cyclic interval-coloring of a multigraph is a proper edge coloring with colors such that the colors of the edges incident with every vertex of are colored by consecutive colors, under the condition that color is considered as consecutive to color . Denote by () and () the minimum and maximum number of colors in a (cyclic) interval coloring of a multigraph , respectively. We present some new sharp bounds on and for multigraphs satisfying various conditions. In particular, we show that if is a -connected multigraph with an interval coloring, then . We also give several results towards the general conjecture that for any triangle-free graph with a cyclic interval coloring; we establish that approximate versions of this conjecture hold for several families of graphs, and we prove that the conjecture is true for graphs with maximum degree at most . 相似文献
12.
Daniel W. Cranston William B. Kinnersley Suil O Douglas B. West 《Discrete Applied Mathematics》2013,161(13-14):1828-1836
13.
Yehong Shao 《Discrete Mathematics》2018,341(12):3441-3446
Let be a graph and be its line graph. In 1969, Chartrand and Stewart proved that , where and denote the edge connectivity of and respectively. We show a similar relationship holds for the essential edge connectivity of and , written and , respectively. In this note, it is proved that if is not a complete graph and does not have a vertex of degree two, then . An immediate corollary is that for such graphs , where the vertex connectivity of the line graph
and the second iterated line graph are written as and respectively. 相似文献
14.
Jianbei An Heiko Dietrich Shih-Chang Huang 《Journal of Pure and Applied Algebra》2018,222(12):4020-4039
We consider the finite exceptional group of Lie type (universal version) with , where and . We classify, up to conjugacy, all maximal-proper 3-local subgroups of G, that is, all 3-local which are maximal with respect to inclusion among all proper subgroups of G which are 3-local. To this end, we also determine, up to conjugacy, all elementary-abelian 3-subgroups containing , all extraspecial subgroups containing , and all cyclic groups of order 9 containing . These classifications are an important first step towards a classification of the 3-radical subgroups of G, which play a crucial role in many open conjectures in modular representation theory. 相似文献
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