Hamilton connectivity of line graphs and claw‐free graphs

Abstract

Abstract Let G be a graph and let V 0 = {ν∈ V ( G ): d G (ν) = 6}. We show in this paper that: (i) if G is a 6‐connected line graph and if | V 0 | ≤ 29 or G [ V 0 ] contains at most 5 vertex disjoint K 4 's, then G is Hamilton‐connected; (ii) every 8‐connected claw‐free graph is Hamilton‐connected. Several related results known before are generalized. © 2005 Wiley Periodicals, Inc. J Graph Theory