共查询到18条相似文献,搜索用时 296 毫秒
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设G是一个2-连通赋权图,且G中每一对不相邻顶点u和v都满足d~w(u)+d~w(v)≥2d.Bondy等人证明了G或者包含一个哈密尔顿圈,或者包含一个权至少为2d的圈.如果G不是哈密尔顿图,这个结论意味着G中包含一个权至少为2d的圈.但是当G是哈密尔顿图时,我们不能判断G是否包含一个权至少为2d的圈.这篇文章中,在Fujisawa的一篇文章的启发下,我们证明了当G是triangle-free图并且|V(G)|是奇数时,G中一定包含一个权至少为2d的圈,即使G是哈密尔顿图. 相似文献
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《数学的实践与认识》2017,(21)
关于平面图的平衡二部子图的研究有一个猜想:任意一n个顶点的平面图G(V,E),必含有一个平衡二部子图G(V_1,V_2)使得e(V_1,V_2)≤n.证明了若n个顶点的哈密尔顿平面图G(V,E)中含有一个近似等边三角形,n≥18,那么G(V,E)必含有一个平衡二部子图G(V_1,V_2)使得e(V_1,V_2)≤n. 相似文献
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《数学的实践与认识》2019,(24)
设G(V,E)是一个图,V_1,V_2是V的一个二部划分,当||V_1|-|V_2||≤1时,称V_1,V_2是V的一个平衡二部划分,用e(V_1,V_2)表示一条边的两个端点在不同划分里边的总数目.最小平衡二部划分是指寻找G(V,E)的一个平衡二部划分使得e(V_1,V_2)最小.研究了二部图和哈密尔顿二部图,得到它们的最小平衡二部划分的上界分别为[m/2]和(n+2)/2. 相似文献
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关于哈密尔顿连通图的一个基本结果是Ore给出的:设G是n阶图,若对于任意两个不相邻顶点u和v,有d(u) d(v)≥n 1,则G是哈密尔顿连通的.设G是一个图,对于任意u (?)V(G),令N(U)=∪_(u∈∪)N(u),d(U)=|N(U)|,称d(U)是U的度.本文利用独立集的度和得到如下结果:设s和t是正整数,G是(2s 2t 1)-连通n阶图.若对于任两个强不交独立集S,T,|S|=s,|T|=t,有d(S) d(T)≥n 1.则G是哈密尔顿连通的.同时也得到图的哈密尔顿性的其它相关结果.两个独立集S和T称为强不交的,如果S∪T也是独立集. 相似文献
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徐新萍 《数学的实践与认识》2009,39(10)
设G是一个图,G的部分平方图G*满足V(G*)=V(G),E(G*)=E(G)∪{uv:uv■E(G),且J(u,v)≠■},这里J(u,v)={w∈N(u)∩N(v):N(w)■N[u]∪N[v]}.利用插点方法,证明了如下结果:设G是k-连通图(k2),b是整数,0min {k,(2b-1+k)/2}(n(Y)-1),则G是哈密尔顿图.同时给出图是1-哈密尔顿的和哈密尔顿连通的相关结果. 相似文献
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在文献[3]中介绍了一个新的图类-P3-支配图.这个图类包含所有的拟无爪图,因此也包含所有的无爪图.在本文中,我们证明了每一个点数至少是3的三角形连通的P3-支配图是哈密尔顿的,但有一个例外图K1,1,3.同时,我们也证明了k-连通的(k≥2)的P3-支配图是哈密尔顿的,如果an(G)≤k,但有两个例外图K1,1,3 and K2,3. 相似文献
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图G称为弱泛圈图是指G包含了每个长为t(g(V)≤l≤c(G))的圈,其中g(G),c(v)分别是G的围长与周长.1997年Brandt提出以下猜想:边数大于[n2/4]-n 5的n阶非二部图为弱泛圈图.1999年Bollobas和Thomason证明了边数不小于[n2/4]-n 59的n阶非二部图为弱泛圈图.作者证明了如下结论:设G是n阶Hamilton非二部图,若G的边数不小于[n2/4]-n 12,则G为弱泛圈图. 相似文献
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Induced subgraphs with large degrees at end-vertices for hamiltonicity of claw-free graphs 下载免费PDF全文
A graph is called claw-free if it contains no induced subgraph isomorphic to K1,3. Matthews and Sumner proved that a 2-connected claw-free graph G is Hamiltonian if every vertex of it has degree at least (|V(G)|-2)/3. At the workshop C&C (Novy Smokovec, 1993), Broersma conjectured the degree condition of this result can be restricted only to end-vertices of induced copies of N (the graph obtained from a triangle by adding three disjoint pendant edges). Fujisawa and Yamashita showed that the degree condition of Matthews and Sumner can be restricted only to end-vertices of induced copies of Z1 (the graph obtained from a triangle by adding one pendant edge). Our main result in this paper is a characterization of all graphs H such that a 2-connected claw-free graph G is Hamiltonian if each end-vertex of every induced copy of H in G has degree at least |V(G)|/3+1. This gives an affirmative solution of the conjecture of Broersma up to an additive constant. 相似文献
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Hamiltonian[k,k+1]-因子 总被引:4,自引:0,他引:4
本文考虑n/2-临界图中Hamiltonian[k,k+1]-因子的存在性。Hamiltonian[k,k+1]-因子是指包含Hamiltonian圈的[k,k+1]-因子;给定阶数为n的简单图G,若δ(G)≥n/2而δ(G\e)相似文献
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高随祥 《应用数学学报(英文版)》2001,17(1):129-139
1. IntroductionA gash G is an ordered pair of disjoillt sets (V, E) such that E is a subset of the setof unordered pairs of V, where the sets V and E are finite. The set V is cajled the setof venices and E is called the set of edges. They are usually denoted by V(G) and E(C),respectively. An edge (x, y) is said to join the venices x and y, and is sometimes denotedby xo or ear. By our definition, a graph does not colltain any loOP, neither does it colltainmultiple edges.Other terms undef… 相似文献
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设λ是图G的一个特征值,如果存在属于λ的一个特征向量X=(x_1,x_2,…,x_n)~T,使得(?)x_i≠0,则λ称为图G的主特征值.将恰有两个主特征值的一个充要条件做了进一步推广,并在此基础上给出恰有两个主特征值的图的一些性质以及恰有两个主特征值的图的一些运算结果. 相似文献
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The problem is considered under which conditions a 4-connected planar or projective planar graph has a Hamiltonian cycle containing certain prescribed edges and missing certain forbidden edges. The results are applied to obtain novel lower bounds on the number of distinct Hamiltonian cycles that must be present in a 5-connected graph that is embedded into the plane or into the projective plane with face-width at least five. Especially, we show that every 5-connected plane or projective plane triangulation on n vertices with no non-contractible cyles of length less than five contains at least distinct Hamiltonian cycles. © 1999 John Wiley & Sons, Inc. J Graph Theory 32: 81–96, 1999 相似文献
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A Hamiltonian path of a graph is a simple path which visits each vertex of the graph exactly once. The Hamiltonian path problem is to determine whether a graph contains a Hamiltonian path. A graph is called Hamiltonian connected if there exists a Hamiltonian path between any two distinct vertices. In this paper, we will study the Hamiltonian connectivity of rectangular supergrid graphs. Supergrid graphs were first introduced by us and include grid graphs and triangular grid graphs as subgraphs. The Hamiltonian path problem for grid graphs and triangular grid graphs was known to be NP-complete. Recently, we have proved that the Hamiltonian path problem for supergrid graphs is also NP-complete. The Hamiltonian paths on supergrid graphs can be applied to compute the stitching traces of computer sewing machines. Rectangular supergrid graphs form a popular subclass of supergrid graphs, and they have strong structure. In this paper, we provide a constructive proof to show that rectangular supergrid graphs are Hamiltonian connected except one trivial forbidden condition. Based on the constructive proof, we present a linear-time algorithm to construct a longest path between any two given vertices in a rectangular supergrid graph. 相似文献
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A triangular grid graph is a finite induced subgraph of the infinite graph associated with the two-dimensional triangular grid. In 2000, Reay and Zamfirescu showed that all 2-connected, linearly-convex triangular grid graphs (with the exception of one of them) are hamiltonian. The only exception is a graph D which is the linearly-convex hull of the Star of David. We extend this result to a wider class of locally connected triangular grid graphs. Namely, we prove that all connected, locally connected triangular grid graphs (with the same exception of graph D) are hamiltonian. Moreover, we present a sufficient condition for a connected graph to be fully cycle extendable. We also show that the problem Hamiltonian Cycle is NP-complete for triangular grid graphs. 相似文献