共查询到20条相似文献,搜索用时 31 毫秒
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Susan A. van Aardt Christoph Brause Alewyn P. Burger Marietjie Frick Arnfried Kemnitz Ingo Schiermeyer 《Discrete Mathematics》2017,340(11):2673-2677
An edge-coloured graph is called properly connected if any two vertices are connected by a path whose edges are properly coloured. The proper connection number of a connected graph denoted by , is the smallest number of colours that are needed in order to make properly connected. Our main result is the following: Let be a connected graph of order and . If , then except when and where and 相似文献
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For bipartite graphs , the bipartite Ramsey number is the least positive integer so that any coloring of the edges of with colors will result in a copy of in the th color for some . In this paper, our main focus will be to bound the following numbers: and for all for and for Furthermore, we will also show that these mentioned bounds are generally better than the bounds obtained by using the best known Zarankiewicz-type result. 相似文献
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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
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Jessica De Silva Kristin Heysse Adam Kapilow Anna Schenfisch Michael Young 《Discrete Mathematics》2018,341(2):492-496
For two graphs and , the Turán number is the maximum number of edges in a subgraph of that contains no copy of . Chen, Li, and Tu determined the Turán numbers for all Chen et al. (2009). In this paper we will determine the Turán numbers for all and . 相似文献
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Jakub Przybyło 《Discrete Mathematics》2018,341(4):1098-1102
Let be a (not necessarily proper) total colouring of a graph with maximum degree . Two vertices are sum distinguished if they differ with respect to sums of their incident colours, i.e. . The least integer admitting such colouring under which every at distance in
are sum distinguished is denoted by . Such graph invariants link the concept of the total vertex irregularity strength of graphs with so-called 1-2-Conjecture, whose concern is the case of . Within this paper we combine probabilistic approach with purely combinatorial one in order to prove that for every integer and each graph , thus improving the previously best result: . 相似文献
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TextFor any given two positive integers and , and any set A of nonnegative integers, let denote the number of solutions of the equation with . In this paper, we determine all pairs of positive integers for which there exists a set such that for all . We also pose several problems for further research.VideoFor a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=EnezEsJl0OY. 相似文献
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