Minimum degree and disjoint cycles in generalized claw-free graphs

Minimum Degree and Disjoint Cycles in Claw-Free Graphs

Vertex disjoint cycles for star free graphs

A graph is claw-free if it does not contain K I ,3 as an induced subgraph. A graph is KI,r-free if it does not contain KI,r as an induced subgraph. In this paper, we find bounds on the minimum number of edges needed to ensure a KI,.,.-free contains k vertex disjoint cycles. The bound on claw-free graphs is sharp.

A note on powers of Hamilton cycles in generalized claw-free graphs

Seymour conjectured for a fixed integer k ≥ 2 that if G is a graph of order n with δ(G) ≥ kn/(k + 1), then G contains the kth power Ck n of a Hamiltonian cycle Cn of G, and this minimum degree condition is sharp. Earlier the k = 2 case was conjectured by Pósa. This was verified by Komlós et al. [4]. For s ≥ 3, a graph is K1,s-free if it does not contain an induced subgraph isomorphic to K1,s. S...

2-factors with Bounded Number of Components in Claw-free Graphs

In this paper, we show that every 3-connected claw-free graph G has a 2-factor having at most max { 2 5(α+1), 1 } cycles, where α is the independence number of G. As a corollary of this result, we also prove that every 3-connected claw-free graph G has a 2-factor with at most ( 4|G| 5(δ+2)+ 2 5 ) cycles, where δ is the minimum degree of G. This is an extension of a known result on the number of...

Hamiltonian cycles in 3-connected Claw-free graphs

It is shown that every 3-connected claw-free graph having at most 6 − 7 vertices is hamiltonian, where is the minimum degree. c © 2002 Elsevier Science B.V. All rights reserved.