共查询到20条相似文献,搜索用时 15 毫秒
1.
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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A Cayley graph on a group is said to be normal if the right regular representation of is normal in the full automorphism group of . In this paper all connected cubic non-normal Cayley graphs of order are constructed explicitly for each odd prime . It is shown that there are three infinite families of cubic non-normal Cayley graphs of order with odd prime. Note that a complete classification of cubic non-Cayley vertex-transitive graphs of order was given in [K. Kutnar, D. Marus?ic?, C. Zhang, On cubic non-Cayley vertex-transitive graphs, J. Graph Theory 69 (2012) 77–95]. As a result, a classification of cubic vertex-transitive graphs of order can be deduced. 相似文献
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In Mader (2010), Mader conjectured that for every positive integer and every finite tree with order , every -connected, finite graph with contains a subtree isomorphic to such that is -connected. In the same paper, Mader proved that the conjecture is true when is a path. Diwan and Tholiya (2009) verified the conjecture when . In this paper, we will prove that Mader’s conjecture is true when is a star or double-star and . 相似文献
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Very recently, Thomassé et al. (2017) have given an FPT algorithm for Weighted Independent Set in bull-free graphs parameterized by the weight of the solution, running in time . In this article we improve this running time to . As a byproduct, we also improve the previous Turing-kernel for this problem from to . Furthermore, for the subclass of bull-free graphs without holes of length at most for , we speed up the running time to . As grows, this running time is asymptotically tight in terms of , since we prove that for each integer , Weighted Independent Set cannot be solved in time in the class of -free graphs unless the ETH fails. 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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Dean Crnković 《Discrete Mathematics》2018,341(2):520-524
Suppose there exists a Hadamard 2- design having skew incidence matrix. If there exists a conference graph on vertices, then there exists a regular Hadamard matrix of order . A conference graph on vertices yields a regular Hadamard matrix of order . 相似文献
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Wei Xiong Jinquan Xu Zhengke Miao Yang Wu Hong-Jian Lai 《Discrete Mathematics》2017,340(12):2995-3001
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In this paper, we employed lattice model to describe the three internally vertex-disjoint paths that span the vertex set of the generalized Petersen graph . We showed that the is 3-spanning connected for odd . Based on the lattice model, five amalgamated and one extension mechanisms are introduced to recursively establish the 3-spanning connectivity of the . In each amalgamated mechanism, a particular lattice trail was amalgamated with the lattice trails that was dismembered, transferred, or extended from parts of the lattice trails for , where a lattice tail is a trail in the lattice model that represents a path in . 相似文献
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This paper is concerned with the quantitative homogenization of 2m-order elliptic systems with bounded measurable, rapidly oscillating periodic coefficients. We establish the sharp convergence rate in with in a bounded Lipschitz domain in as well as the uniform large-scale interior estimate. With additional smoothness assumptions, the uniform interior , and estimates are also obtained. As applications of the regularity estimates, we establish asymptotic expansions for fundamental solutions. 相似文献
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The decycling number of a graph is the smallest number of vertices which can be removed from so that the resultant graph contains no cycle. A decycling set containing exactly vertices of is called a -set. For any decycling set of a -regular graph , we show that , where is the cycle rank of , is the margin number of , and are, respectively, the number of components of and the number of edges in . In particular, for any -set of a 3-regular graph , we prove that , where is the Betti deficiency of . This implies that the decycling number of a 3-regular graph is . Hence for a 3-regular upper-embeddable graph , which concludes the results in [Gao et al., 2015, Wei and Li, 2013] and solves two open problems posed by Bau and Beineke (2002). Considering an algorithm by Furst et al., (1988), there exists a polynomial time algorithm to compute , the cardinality of a maximum nonseparating independent set in a -regular graph , which solves an open problem raised by Speckenmeyer (1988). As for a 4-regular graph , we show that for any -set of , there exists a spanning tree of such that the elements of are simply the leaves of with at most two exceptions providing . On the other hand, if is a loopless graph on vertices with maximum degree at most , then The above two upper bounds are tight, and this makes an extension of a result due to Punnim (2006). 相似文献
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A set of vertices in a graph is an independent dominating set of if is an independent set and every vertex not in is adjacent to a vertex in . The independent domination number, , of is the minimum cardinality of an independent dominating set. In this paper, we extend the work of Henning, Löwenstein, and Rautenbach (2014) who proved that if is a bipartite, cubic graph of order and of girth at least , then . We show that the bipartite condition can be relaxed, and prove that if is a cubic graph of order and of girth at least , then . 相似文献
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The distinguishing chromatic number of a graph , denoted , is defined as the minimum number of colors needed to properly color such that no non-trivial automorphism of fixes each color class of . In this paper, we consider random Cayley graphs defined over certain abelian groups with , and show that with probability at least , . 相似文献
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The edge-intersection graph of a family of paths on a host tree is called an graph. When the tree has maximum degree , we say that the graph is . If, in addition, the family of paths satisfies the Helly property, then the graph is Helly . In this paper, we present a family of graphs called gates which are forbidden induced subgraphs for graphs. Using these we characterize by forbidden induced subgraphs the Helly graphs. As a byproduct we prove that in getting a Helly -representation, it is not necessary to increase the maximum degree of the host tree. In addition, we give an efficient algorithm to recognize Helly graphs based on their decomposition by maximal clique separators. 相似文献
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A spanning tree of a properly edge-colored complete graph, , is rainbow provided that each of its edges receives a distinct color. In 1996, Brualdi and Hollingsworth conjectured that if is properly -edge-colored, then the edges of can be partitioned into rainbow spanning trees except when . By means of an explicit, constructive approach, in this paper we construct mutually edge-disjoint rainbow spanning trees for any positive value of . Not only are the rainbow trees produced, but also some structure of each rainbow spanning tree is determined in the process. This improves upon best constructive result to date in the literature which produces exactly three rainbow trees. 相似文献
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Yian Xu 《Discrete Mathematics》2017,340(12):2972-2977
Bamberg and Giudici (2011) showed that the point graphs of certain generalised quadrangles of order , where is a prime power with , are both normal and non-normal Cayley graphs for two isomorphic groups. We call these graphs BG-graphs. In this paper, we show that the Cayley graphs obtained from a finite number of BG-graphs by Cartesian product, direct product, and strong product also possess the property of being normal and non-normal Cayley graphs for two isomorphic groups. 相似文献