## Abstract Our main result is the following theorem. Let __k__โโฅโ2 be an integer, __G__ be a graph of sufficiently large order __n__, and __ฮด__(__G__)โโฅโ__n__/__k__. Then: __G__ contains a cycle of length __t__ for every even integer __t__โโโ[4, __ฮด__(__G__)โ+โ1]. If __G__ is nonbipartite then
Contractible cycles in graphs with large minimum degree
โ Scribed by Yoshimi Egawa
- Book ID
- 108316044
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 717 KB
- Volume
- 171
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
A cycle C of a graph G is a D~-cycle if every component of G-V(C) has order less than 2. Using the notion of D~-cycles, a number of results are established concerning long cycles in graphs with prescribed toughness and minimum degree. Let G be a t-tough graph on n/> 3 vertices. If 6 > n/(t + 2) + 2-
## Abstract Let __G__ be a simple graph of order __n__ and minimal degree >โcn (0โ<โcโ<โ1/2). We prove that (1) There exist __n__~0~โ=โ__n__~0~(__c__) and __k__โ=โ__k__(__c__) such that if __n__โ>โ__n__~0~ and __G__ contains a cycle __C__~__t__~ for some __t__โ>โ2__k__, then __G__ contains a cycle
Let k 3 be an integer. We show that if G is a k-connected graph with girth at least 5, then G has an induced cycle Q such that G&V(Q) is (k&1)-connected. 1998 Academic Press ## 1. Introduction By a graph, we mean a finite, undirected, simple graph with no loops and no multiple edges. Let G=(V(G