排序方式: 共有12条查询结果,搜索用时 15 毫秒
1.
Cycle embedding in star graphs with conditional edge faults 总被引:1,自引:0,他引:1
Ming-Chien Yang 《Applied mathematics and computation》2010,215(10):3541-3867
Among the various interconnection networks, the star graph has been an attractive one. In this paper, we consider the cycle embedding problem in star graphs with conditional edge faults. We show that there exist cycles of all even lengths from 6 to n! in an n-dimensional star graph with ?2n-7 edge faults in which each vertex is incident with at least two healthy edges for n?4. 相似文献
2.
Given a graph , let be the set of all cycle lengths contained in and let . Let and let be the greatest common divisor of and all the positive pairwise differences of elements in . We prove that if a Hamiltonian graph of order has at least edges, where is an integer such that , then or is exceptional, by which we mean for some . We also discuss cases where is not exceptional, for example when is prime. Moreover, we show that , which if is bipartite implies that , where is the number of edges in . 相似文献
3.
Ahmed Ainouche 《Graphs and Combinatorics》2009,25(2):129-137
Let G = (V, E) be a any simple, undirected graph on n ≥ 3 vertices with the degree sequence . We consider the class of graphs satisfying the condition where , is a positive integer. It is known that is hamiltonian if θ ≤ δ. In this paper,
相似文献
(i) | we give a necessary and sufficient condition, easy to check, ensuring that is nonhamiltonian and we characterize all the exceptional sub-classes. |
(ii) | we prove that is either bipartite or contains cycles of all lengths from 3 to c(G), the length of a longest cycle in G. |
4.
Mariusz Meszka 《Discrete Mathematics》2018,341(11):3237-3240
The main results provide sufficient conditions for balanced bipartite digraphs to be bipancyclic. These are analogues to well-known results on pancyclic digraphs. 相似文献
5.
A cycle of order is called a -cycle. A non-induced cycle is called a chorded cycle. Let be an integer with . Then a graph of order is chorded pancyclic if contains a chorded -cycle for every integer with . Cream, Gould and Hirohata (Australas. J. Combin. 67 (2017), 463–469) proved that a graph of order satisfying for every pair of nonadjacent vertices , in is chorded pancyclic unless is either or , the Cartesian product of and . They also conjectured that if is Hamiltonian, we can replace the degree sum condition with the weaker density condition
and still guarantee the same conclusion. In this paper, we prove this conjecture by showing that if a graph of order with contains a -cycle, then contains a chorded -cycle, unless and is either or , Then observing that and are exceptions only for , we further relax the density condition for sufficiently large . 相似文献
6.
7.
Given integers k,s,t with 0≤s≤t and k≥0, a (k,t,s)-linear forest F is a graph that is the vertex disjoint union of t paths with a total of k edges and with s of the paths being single vertices. If the number of single vertex paths is not critical, the forest F will simply be called a (k,t)-linear forest. A graph G of order n≥k+t is (k,t)-hamiltonian if for any (k,t)-linear forest F there is a hamiltonian cycle containing F. More generally, given integers m and n with k+t≤m≤n, a graph G of order n is (k,t,s,m)-pancyclic if for any (k,t,s)-linear forest F and for each integer r with m≤r≤n, there is a cycle of length r containing the linear forest F. Minimum degree conditions and minimum sum of degree conditions of nonadjacent vertices that imply that a graph is (k,t,s,m)-pancyclic (or just (k,t,m)-pancyclic) are proved. 相似文献
8.
We call a graph pancyclic if it contains at least one cycle of every possible length , for . In this paper, we define a new property called chorded pancyclicity. We explore forbidden subgraphs in claw-free graphs sufficient to imply that the graph contains at least one chorded cycle of every possible length . In particular, certain paths and triangles with pendant paths are forbidden. 相似文献
9.
For a graph G, let σ2(G) denote the minimum degree sum of two nonadjacent vertices (when G is complete, we let σ2(G)=∞). In this paper, we show the following two results: (i) Let G be a graph of order n≥4k+3 with σ2(G)≥n and let F be a matching of size k in G such that G−F is 2-connected. Then G−F is hamiltonian or G≅K2+(K2∪Kn−4) or ; (ii) Let G be a graph of order n≥16k+1 with σ2(G)≥n and let F be a set of k edges of G such that G−F is hamiltonian. Then G−F is either pancyclic or bipartite. Examples show that first result is the best possible. 相似文献
10.
Let n and be two integers such that 2n–1. We describe the set of cycle lengths occurring in any hamiltonian graph G of order n and maximum degree . We conclude that for the case this set contains all the integers belonging to the union [3,2–n+2][n–+2,+1], and for it contains every integer between 3 and +1. We also study the set of cycle lengths in a hamiltonian graph with two fixed vertices of large degree sum. Our main results imply that the stability s(P) for the property of being pancyclic satisfies 相似文献