共查询到20条相似文献,搜索用时 78 毫秒
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研究子图的度和图的哈密尔顿性的关系,证明图~$G$ 是一个~$n$ 阶~3-\,连通无爪图且最小度~$\delta(G)\geq4$, 如果图~$G$ 中任意两个分别同构于~$P_4$, $K_1$ 的不相邻子图~$H_1$, $H_2$ 满足~$d(H_1)+d(H_2)\geq n$, 则图~$G$ 是哈密尔顿连通. 相似文献
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设H是图G的一个子图.图G中同构于H的点不交的子图构成的集合称为G的一个H-匹配.图G的H-匹配的最大基数称为是G的H-匹配数,记为ν(H,G).本文主要研究ν(H,G)与G的无符号拉普拉斯谱的关系,同时也讨论了ν(H,G)与G的拉普拉斯谱的关系. 相似文献
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子图识别问题(SRP)就是在一个图G中确定并寻找是否存在和另一个图H相同构的子图.本文将引入图的层分解概念,并以此为基础建立识别图的同构子图的算法.该算法的复杂性为O(n(△-1)^k-1),其中△是图G的度,即G中点的最大度,n,k分别是图G,H的阶. 相似文献
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这里考虑的是简单图.图 G 的 K_k-因子是 G 的这样一种支撑子图,它的每个连通片皆同构于 k 个节点的完全图 K_k.本文给出:如果 G 具有唯一的 K_k-因子,则|E(G)|≤n~2·k(k-1)/2;进而,对于|E(G)|=n~2·k(k-1)/2的图 G 完全确定了 G 的结构. 相似文献
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Bhalchandra D. Thatte 《Journal of Graph Theory》2020,93(2):181-202
Previously we showed that many invariants of a graph can be computed from its abstract induced subgraph poset, which is the isomorphism class of the induced subgraph poset, suitably weighted by subgraph counting numbers. In this paper, we study the abstract bond lattice of a graph, which is the isomorphism class of the lattice of distinct unlabelled connected partitions of a graph, suitably weighted by subgraph counting numbers. We show that these two abstract posets can be constructed from each other except in a few trivial cases. The constructions rely on certain generalisations of a lemma of Kocay in graph reconstruction theory to abstract induced subgraph posets. As a corollary, trees are reconstructible from their abstract bond lattice. We show that the chromatic symmetric function and the symmetric Tutte polynomial of a graph can be computed from its abstract induced subgraph poset. Stanley has asked if every tree is determined up to isomorphism by its chromatic symmetric function. We prove a counting lemma, and indicate future directions for a study of Stanley's question. 相似文献
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CHENHUAITANG MAKEJIE 《高校应用数学学报(英文版)》1998,13(2):165-170
The definition of the ascending suhgraph decomposition was given by Alavi. It has been conjectured that every graph of positive size has an ascending subgraph decomposition. In this paper it is proved that the regular graphs under some conditions do have an ascending subgraph decomposition. 相似文献
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We present a characterization of level planar graphs in terms of minimal forbidden subgraphs called minimal level non-planar (MLNP) subgraph patterns. We show that an MLNP subgraph pattern is completely characterized by either a tree, a level non-planar cycle or a level planar cycle with certain path augmentations. 相似文献
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It is known that a class of graphs defined by a single forbidden induced subgraph G is well-quasi-ordered by the induced subgraph relation if and only if G is an induced subgraph of P4. However, very little is known about well-quasi-ordered classes of graphs defined by more than one forbidden induced subgraph. We conjecture that for any natural number k, there are finitely many minimal classes of graphs defined by k forbidden induced subgraphs which are not well-quasi-ordered by the induced subgraph relation and prove the conjecture for k=2. We explicitly reveal many of the minimal classes defined by two forbidden induced subgraphs which are not well-quasi-ordered and many of those which are well-quasi-ordered by the induced subgraph relation. 相似文献
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A parity subgraph of a graph is a spanning subgraph such that the degrees of each vertex have the same parity in both the subgraph and the original graph. Known results include that every graph has an odd number of minimal parity subgraphs. Define a disparity subgraph to be a spanning subgraph such that each vertex has degrees of opposite parities in the subgraph and the original graph. (Only graphs with all even-order components can have disparity subgraphs). Every even-order spanning tree contains both a unique parity subgraph and a unique disparity subgraph. Moreover, every minimal disparity subgraph is shown to be paired by sharing a spanning tree with an odd number of minimal parity subgraphs, and every minimal parity subgraph is similarly paired with either one or an even number of minimal disparity subgraphs. 相似文献
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Maria Chudnovsky Paul Seymour Sophie Spirkl Mingxian Zhong 《Discrete Mathematics》2018,341(8):2179-2196
The graphs with no five-vertex induced path are still not understood. But in the triangle-free case, we can do this and one better; we give an explicit construction for all triangle-free graphs with no six-vertex induced path. Here are three examples: the 16-vertex Clebsch graph, the graph obtained from an 8-cycle by making opposite vertices adjacent, and the graph obtained from a complete bipartite graph by subdividing a perfect matching. We show that every connected triangle-free graph with no six-vertex induced path is an induced subgraph of one of these three (modulo some twinning and duplication). 相似文献
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A graph is polar if the vertex set can be partitioned into A and B in such a way that the subgraph induced by A is a complete multipartite graph and the subgraph induced by B is a disjoint union of cliques. Polar graphs are a common generalization of bipartite, cobipartite, and split graphs. However, recognizing polar graphs is an NP-complete problem in general. This led to the study of the polarity of special classes of graphs such as cographs and chordal graphs, cf. Ekim et al. (2008) [7] and [5]. In this paper, we study the polarity of line graphs and call a graph line-polar if its line graph is polar. We characterize line-polar bipartite graphs in terms of forbidden subgraphs. This answers a question raised in the fist reference mentioned above. Our characterization has already been used to develop a linear time algorithm for recognizing line-polar bipartite graphs, cf. Ekim (submitted for publication) [6]. 相似文献
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Qian Kong 《Discrete Mathematics》2010,310(24):3523-3527
Let Γ denote a distance-regular graph with a strongly closed regular subgraph Y. Hosoya and Suzuki [R. Hosoya, H. Suzuki, Tight distance-regular graphs with respect to subsets, European J. Combin. 28 (2007) 61-74] showed an inequality for the second largest and least eigenvalues of Γ in the case Y is of diameter 2. In this paper, we study the case when Γ is bipartite and Y is of diameter 3, and obtain an inequality for the second largest eigenvalue of Γ. Moreover, we characterize the distance-regular graphs with a completely regular strongly closed subgraph H(3,2). 相似文献
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Du
an Hvalica 《Discrete Applied Mathematics》2001,110(2-3):213-225
An algorithm for searching for a minimal solution subgraph in AND/OR graphs with cycles is described, which works top–down and is appropriate to explicit AND/OR graphs. 相似文献
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Keith Edwards 《Discrete Mathematics》2008,308(12):2396-2406
The coefficient of fragmentability of a class of graphs measures the proportion of vertices that need to be removed from the graphs in the class in order to leave behind bounded sized components. We have previously given bounds on this parameter for the class of graphs satisfying a given constant bound on maximum degree. In this paper, we give fragmentability bounds for some classes of graphs of bounded average degree, as well as classes of given thickness, the class of k-colourable graphs, and the class of n-dimensional cubes. In order to establish the fragmentability results for bounded average degree, we prove that the proportion of vertices that must be removed from a graph of average degree at most in order to leave behind a planar subgraph (in fact, a series-parallel subgraph) is at most , provided or the graph is connected and . The proof yields an algorithm for finding large induced planar subgraphs and (under certain conditions) a lower bound on the size of the induced planar subgraph it finds. This bound is similar in form to the one we found for a previous algorithm we developed for that problem, but applies to a larger class of graphs. 相似文献