共查询到20条相似文献,搜索用时 15 毫秒
1.
2.
Iain Moffatt 《Annals of Combinatorics》2016,20(2):373-378
We give an excluded minor characterisation of the class of ribbon graphs that admit partial duals of Euler genus at most one. 相似文献
3.
In a previous paper (J. Combin. Theory 48 (1990) 255) we showed that for any infinite set of (finite) graphs drawn in a fixed surface, one of the graphs is isomorphic to a minor of another. In this paper we extend that result in two ways:
- • we generalize from graphs to hypergraphs drawn in a fixed surface, in which each edge has two or three ends, and
- • the edges of our hypergraphs are labelled from a well-quasi-order, and the minor relation is required to respect this order.
4.
Ralph J. Faudree Ronald J. Gould Michael S. Jacobson Douglas B. West 《Journal of Graph Theory》2017,84(2):202-213
A dominating path in a graph is a path P such that every vertex outside P has a neighbor on P. A result of Broersma from 1988 implies that if G is an n‐vertex k‐connected graph and , then G contains a dominating path. We prove the following results. The lengths of dominating paths include all values from the shortest up to at least . For , where a is a constant greater than 1/3, the minimum length of a dominating path is at most logarithmic in n when n is sufficiently large (the base of the logarithm depends on a). The preceding results are sharp. For constant s and , an s‐vertex dominating path is guaranteed by when n is sufficiently large, but (where ) does not even guarantee a dominating set of size s. We also obtain minimum‐degree conditions for the existence of a spanning tree obtained from a dominating path by giving the same number of leaf neighbors to each vertex. 相似文献
5.
Raffaele Mosca 《Graphs and Combinatorics》2001,17(3):517-528
Let G be a graph with n vertices, and denote as γ(G) (as θ(G)) the cardinality of a minimum edge cover (of a minimum clique cover) of G. Let E (let C) be the edge-vertex (the clique-vertex) incidence matrix of G; write then P(E)={x∈ℜ
n
:Ex≤1,x≥0}, P(C)={x∈ℜ
n
:Cx≤1,x≥0}, α
E
(G)=max{1
T
x subject to x∈P(E)}, and α
C
(G)= max{1
T
x subject to x∈P(C)}. In this paper we prove that if α
E
(G)=α
C
(G), then γ(G)=θ(G).
Received: May 20, 1998?Final version received: April 12, 1999 相似文献
6.
7.
8.
本文证明了:设G是n阶、k(≥3)连通无爪图,且不含同构于B的导出子图,若存在点v_0∈V(G),使d(v_0)≥n-2k+4,则G是Hamilton连通的. 相似文献
9.
The kth power of a simple graph G, denoted by , is the graph with vertex set where two vertices are adjacent if they are within distance k in G. We are interested in finding lower bounds on the average degree of . Here we prove that if G is connected with minimum degree and , then G4 has average degree at least . We also prove that if G is a connected d‐regular graph on n vertices with diameter at least , then the average degree of is at least Both these results are shown to be essentially best possible; the second is best possible even when is arbitrarily large. 相似文献
10.
Paul A. Catlin 《Journal of Graph Theory》1978,2(2):165-170
We show that the vertex set of any graph G with p?2 vertices can be partitioned into non-empty sets V1, V2, such that the maximum degree of the induced subgraph 〈Vi〉 does not exceed where pi = |Vi|, for i=1, 2. Furthermore, the structure of the induced subgraphs is investigated in the extreme case. 相似文献
11.
12.
Herbert Fleischner 《Journal of Graph Theory》2014,75(2):167-177
We construct an infinite family of uniquely hamiltonian graphs of minimum degree 4, maximum degree 14, and of arbitrarily high maximum degree. 相似文献
13.
We consider variants of the triangle-avoidance game first defined by Harary and rediscovered by Hajnal a few years later. A graph game begins with two players and an empty graph on n vertices. The two players take turns choosing edges within K n , building up a simple graph. The edges must be chosen according to a set of restrictions ${\mathcal{R}}$ . The winner is the last player to choose an edge that does not violate any of the restrictions in ${\mathcal{R}}$ . For fixed n and ${\mathcal{R}}$ , one of the players has a winning strategy. For various games where ${\mathcal{R}}$ includes bounded degree and triangle avoidance, we determine the winner for all values of n. 相似文献
14.
Let G=(V,E) be a simple graph. A subset D⊆V is a dominating set of G, if for any vertex x ∈ V−D, there exists a vertex y ∈ D such that xy ∈ E. By using the so-called vertex disjoint paths cover introduced by Reed, in this paper we prove that every graph G on n vertices with minimum degree at least five has a dominating set of order at most 5n/14. 相似文献
15.
设U (n)是具有n个顶点的所有单圈图的集合,G(3; n- 3)是由一个三角形C3粘上一条悬挂路P_(n-3)得到的单圈图.本文将证明当n 5时具有最大度距离的单圈图是G(3; n - 3). 相似文献
16.
一类无标度随机图的度序列 总被引:1,自引:0,他引:1
本文从-个新的角度对-类随机图的度序列进行了分析.证明了此模型度分布的存在性,得到了网络规模比较大的情况下度为七的节点所占比例数的表达式.此外,我们还将模型扩展到每个时间步增加边数为随机变量的情形,得到了类似的结论. 相似文献
17.
We present a tight extremal threshold for the existence of Hamilton cycles in graphs with large minimum degree and without a large “bipartite hole” (two disjoint sets of vertices with no edges between them). This result extends Dirac's classical theorem, and is related to a theorem of Chvátal and Erd?s. In detail, an ‐bipartite‐hole in a graph G consists of two disjoint sets of vertices S and T with and such that there are no edges between S and T ; and is the maximum integer r such that G contains an ‐bipartite‐hole for every pair of nonnegative integers s and t with . Our central theorem is that a graph G with at least three vertices is Hamiltonian if its minimum degree is at least . From the proof we obtain a polynomial time algorithm that either finds a Hamilton cycle or a large bipartite hole. The theorem also yields a condition for the existence of k edge‐disjoint Hamilton cycles. We see that for dense random graphs , the probability of failing to contain many edge‐disjoint Hamilton cycles is . Finally, we discuss the complexity of calculating and approximating . 相似文献
18.
模糊拟阵的基图是模糊拟阵的基本概念.在准模糊图拟阵的基础上,给出了准模糊图拟阵基图的相邻的次限制最小基的一些性质.将为深入研究模糊拟阵的内在本质,进一步研究模糊拟阵的算法奠定了基础. 相似文献
19.
20.
最小次数至少为4的超欧拉图 总被引:4,自引:0,他引:4
设G是2-边-连通的n阶图。假设对任何的的最小边割集E等于包含于E(G)且│E│≤3,G-E的每个分支的阶至少为n/5,则或者G是一个超欧拉图或者G有5个互不相交的阶数为n/5连通分支,当这5个分支都收缩时,G收缩为K2,3,这个结果推广了蔡小涛,P.A.Catlin,F.Jaeger和H.J.Lai等人关于超欧拉图的结果。 相似文献