共查询到18条相似文献,搜索用时 46 毫秒
1.
2.
Dirac定理的局部化与Hamilton图 总被引:4,自引:0,他引:4
设G为一个n阶2-连通图,n≥3.若|Dn/2(K1,3)|≥2且满足下述条件之一:i)|Dn/2(K1,3+e)|≥2,ii)若K1,3+e→G,xy(?)E(K1,3+e),则max{dG(x),dG(y)}≥n/2,则G是一个Hamiltonian图或其闭包为sP|⊕H,这里sP⊕H是一类极小2-边连通图. 相似文献
3.
4.
5.
图G的Alon-Tarsi数,是指最小的k使得G存在一个最大出度不大于k-1的定向D满足G的奇支撑欧拉子图的个数不同于偶支撑欧拉子图的个数.通过分析Halin图的结构,利用Alon-Tarsi定向的方法确定了Halin图的Alon-Tarsi数. 相似文献
6.
The Q-index of a graph G is the largest eigenvalue q(G) of its signless Laplacian matrix Q(G). In this paper, we prove that the wheel graph W_n = K_1 ∨C_(n-1)is the unique graph with maximal Q-index among all Halin graphs of order n. Also we obtain the unique graph with second maximal Q-index among all Halin graphs of order n. 相似文献
7.
Let G be a3-connected graph with n vertices.The paper proves that if for each pair of verti-ces u and v of G,d(u,v)=2,has|N(u)∩N(v)|≤α(αis the minimum independent set num-ber),and then max{d(u),d(v)|≥n 1/2,then G is a Hamilton connected graph. 相似文献
8.
Hamilton图的特定生成了图问题的反例 总被引:1,自引:1,他引:0
[1]定理3断言:一个Hamilton图G必存在仅有p条桥的相间偶圈,如果相间偶圈的边中有边在G的p个不连通初等子圈上(p≥2)。本的反例表明上述结论是错的,从而[1]中关于Peterson图不是Hamilton图的证明也不成立。 相似文献
9.
设G=(V,E)为简单图,δ为图G的最小度,1987年Faudree等人给出NC=min{|N(x)∪N(y)‖x,y∈V(G),xy∈N(G)},有关文献曾研究3连通的H连通图,本文进一步得到:若G是n阶2连通图,且NC≥n-δ,则G除几个图外均是H连通图,从而,完成了邻并条件的H连通图问题。 相似文献
10.
图G的线性点荫度vla(G)是指V(G)的最小划分数,使得每个点划分集的导出子图为线性森林.G的线性k-点荫度vlak(G)是指V(G)的最小划分数,使得每个点划分集的导出子图的每个连通分支为长度至多为k的路.1998年,吴建良证明了Halin图的线性点荫度为2.本文在此基础上,证明了对Halin图G,有vlak(G)=2,其中■ 相似文献
11.
A k-dimensional box is the Cartesian product R1×R2×?×Rk where each Ri is a closed interval on the real line. The boxicity of a graph G, denoted as is the minimum integer k such that G is the intersection graph of a collection of k-dimensional boxes. Halin graphs are the graphs formed by taking a tree with no degree 2 vertex and then connecting its leaves to form a cycle in such a way that the graph has a planar embedding. We prove that if G is a Halin graph that is not isomorphic to K4, then . In fact, we prove the stronger result that if G is a planar graph formed by connecting the leaves of any tree in a simple cycle, then unless G is isomorphic to K4 (in which case its boxicity is 1). 相似文献
12.
We investigate graphs G such that the line graph L(G) is hamiltonian connected if and only if L(G) is 3-connected, and prove that if each 3-edge-cut contains an edge lying in a short cycle of G, then L(G) has the above mentioned property. Our result extends Kriesell’s recent result in [M. Kriesell, All 4-connected line graphs of claw free graphs are hamiltonian-connected, J. Combin. Theory Ser. B 82 (2001) 306-315] that every 4-connected line graph of a claw free graph is hamiltonian connected. Another application of our main result shows that if L(G) does not have an hourglass (a graph isomorphic to K5−E(C4), where C4 is an cycle of length 4 in K5) as an induced subgraph, and if every 3-cut of L(G) is not independent, then L(G) is hamiltonian connected if and only if κ(L(G))≥3, which extends a recent result by Kriesell [M. Kriesell, All 4-connected line graphs of claw free graphs are hamiltonian-connected, J. Combin. Theory Ser. B 82 (2001) 306-315] that every 4-connected hourglass free line graph is hamiltonian connected. 相似文献
13.
Peter F. Stadler 《Journal of Graph Theory》2003,43(2):150-155
Halin graphs are planar 3‐connected graphs that consist of a tree and a cycle connecting the end vertices of the tree. It is shown that all Halin graphs that are not “necklaces” have a unique minimum cycle basis. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 150–155, 2003 相似文献
14.
A graph, G, is called uniquely Hamiltonian if it contains exactly one Hamilton cycle. We show that if G=(V, E) is uniquely Hamiltonian then
Where #(G)=1 if G has even number of vertices and 2 if G has odd number of vertices. It follows that every n-vertex uniquely Hamiltonian graph contains a vertex whose degree is at most c log2n+2 where c=(log23−1)−1≈1.71 thereby improving a bound given by Bondy and Jackson [3]. 相似文献
15.
16.
It is known that the edge set of a 2-edge-connected 3-regular graph can be decomposed into paths of length 3. W. Li asked
whether the edge set of every 2-edge-connected graph can be decomposed into paths of length at least 3. The graphs C
3, C
4, C
5, and K
4−e have no such decompositions. We construct an infinite sequence {F
i
}
i=0
∞
of nondecomposable graphs. On the other hand, we prove that every other 2-edge-connected graph has a desired decomposition.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
17.
18.
图G中同构于K_(1,p)的子图叫G的p-爪(p≥3).如果G中任意一个p-爪中1度顶点之间边(在G中的边)的数目≥p-2,则称G为K(1,p-)-受限图,它是无爪图(p=3)时的推广.本文证明了:连通的K_(1,4-)受限图G,若|G|≥7,则G有Hamilton路或有长至少为2δ+2的路. 相似文献