共查询到20条相似文献,搜索用时 949 毫秒
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Ju Zhou 《Discrete Mathematics》2018,341(4):1021-1031
A graph is induced matching extendable or IM-extendable if every induced matching of is contained in a perfect matching of . In 1998, Yuan proved that a connected IM-extendable graph on vertices has at least edges, and that the only IM-extendable graph with vertices and edges is , where is an arbitrary tree on vertices. In 2005, Zhou and Yuan proved that the only IM-extendable graph with vertices and edges is , where is an arbitrary tree on vertices and is an edge connecting two vertices that lie in different copies of and have distance 3 between them in . In this paper, we introduced the definition of -joint graph and characterized the connected IM-extendable graphs with vertices and edges. 相似文献
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For a 3-edge-connected cubic graph , we give an algorithm to construct a connected Eulerian subgraph of using at most edges. 相似文献
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Jeong-Hyun Kang 《Discrete Mathematics》2018,341(1):96-103
The vertices of Kneser graph are the subsets of of cardinality , two vertices are adjacent if and only if they are disjoint. The square of a graph is defined on the vertex set of with two vertices adjacent if their distance in is at most 2. Z. Füredi, in 2002, proposed the problem of determining the chromatic number of the square of the Kneser graph. The first non-trivial problem arises when . It is believed that where is a constant, and yet the problem remains open. The best known upper bounds are by Kim and Park: for 1 (Kim and Park, 2014) and for (Kim and Park, 2016). In this paper, we develop a new approach to this coloring problem by employing graph homomorphisms, cartesian products of graphs, and linear congruences integrated with combinatorial arguments. These lead to , where is a constant in , depending on . 相似文献
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A graph is minimally -tough if the toughness of is and the deletion of any edge from decreases the toughness. Kriesell conjectured that for every minimally -tough graph the minimum degree . We show that in every minimally -tough graph . We also prove that every minimally -tough, claw-free graph is a cycle. On the other hand, we show that for every positive rational number any graph can be embedded as an induced subgraph into a minimally -tough graph. 相似文献
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Xue-gang Chen Shinya Fujita Michitaka Furuya Moo Young Sohn 《Discrete Applied Mathematics》2012,160(4-5):488-493
A graph is said to be bicritical if the removal of any pair of vertices decreases the domination number of . For a bicritical graph with the domination number , we say that is -bicritical. Let denote the edge-connectivity of . In [2], Brigham et al. (2005) posed the following question: If is a connected bicritical graph, is it true that In this paper, we give a negative answer toward this question; namely, we give a construction of infinitely many connected -bicritical graphs with edge-connectivity for every integer . Furthermore, we give some sufficient conditions for a connected -bicritical graph to have . 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
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Let be a finite group, written multiplicatively. The Davenport constant of is the smallest positive integer such that every sequence of with elements has a non-empty subsequence with product . Let be the Dihedral Group of order and be the Dicyclic Group of order . Zhuang and Gao (2005) showed that and Bass (2007) showed that . In this paper, we give explicit characterizations of all sequences of such that and is free of subsequences whose product is 1, where is equal to or for some . 相似文献
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Let be a plane graph, and let be a colouring of its edges. The edge colouring of is called facial non-repetitive if for no sequence , , of consecutive edge colours of any facial path we have for all . Assume that each edge of a plane graph is endowed with a list of colours, one of which has to be chosen to colour . The smallest integer such that for every list assignment with minimum list length at least there exists a facial non-repetitive edge colouring of with colours from the associated lists is the facial Thue choice index of , and it is denoted by . In this article we show that for arbitrary plane graphs . Moreover, we give some better bounds for special classes of plane graphs. 相似文献
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A note on degree sum conditions for 2-factors with a prescribed number of cycles in bipartite graphs
Let be a balanced bipartite graph of order , and let be the minimum degree sum of two non-adjacent vertices in different partite sets of . In 1963, Moon and Moser proved that if , then is hamiltonian. In this note, we show that if is a positive integer, then the Moon–Moser condition also implies the existence of a 2-factor with exactly cycles for sufficiently large graphs. In order to prove this, we also give a condition for the existence of vertex-disjoint alternating cycles with respect to a chosen perfect matching in . 相似文献
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Haiyang Zhu Lianying Miao Sheng Chen Xinzhong Lü Wenyao Song 《Discrete Mathematics》2018,341(8):2211-2219
Let be the set of all positive integers. A list assignment of a graph is a function that assigns each vertex a list for all . We say that is --choosable if there exists a function such that for all , if and are adjacent, and if and are at distance 2. The list--labeling number of is the minimum such that for every list assignment , is --choosable. We prove that if is a planar graph with girth
and its maximum degree is large enough, then . There are graphs with large enough and having . 相似文献
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Talmage J. Reid Jakayla Robbins Haidong Wu Xiangqian Zhou 《Discrete Mathematics》2010,310(17-18):2389-2397