On traceability and 2-factors in claw-free graphs
Dalibor Fronček, Zdeněk Ryjáček, Zdzisław Skupień · Discussiones Mathematicae Graph Theory · 2004
If G is a claw-free graph of sufficiently large order n, satisfying a degree condition oe k ? n + k \\Gamma 4k + 7 (where k is an arbitrary constant), then G has a 2-factor with at most k \\Gamma 1 components. As a second main result, we present classes of graphs C 1 ; : : : ; C 8 such that every sufficiently large connected claw-free graph satisfying degree condition oe 6 (k) ? n+19 (or, as a corollary, ffi (G) ? n+19 ) either belongs to [ i=1 C i or is traceable.