Sufficient degree conditions for traceability of claw-free graphs

We present new results on the traceability of claw-free graphs. In particular, we consider sufficient minimum degree and degree sum conditions that imply that these graphs admit a Hamilton path, unless they have a small order or they belong to well-defined classes of exceptional graphs. Our main result implies that a 2-connected claw-free graph G of sufficiently large order n with minimum degree d(G) = 22 is traceable if the degree sum of any set of t independent vertices of G is at least ^t(2ⁿ₁₄^-5) , where t ? {1, 2, . . ., 7}, unless G belongs to one of a number of well-defined classes of exceptional graphs depending on t. Our results also imply that a 2-connected claw-free graph G of sufficiently large order n with d(G) = 18 is traceable if the degree sum of any set of six independent vertices is larger than n - 6, and that this lower bound on the degree sums is sharp.