A Note on Hamiltonian Cycles in (k,n)-Factor-Critical Graphs
Ken‐ichi Kawarabayashi · SUT Journal of Mathematics · 2000
A graph G is said to be (k,n)-factor-critical if G−S has a k-factor for any S⊂V(G) with |S|=n. In [7], the author, Ota and Saito conjectured that if G is a 2-connected (k,n)-factor-critical graph of order p with σ3(G)≥32(p−n−k), then G is hamiltonian with some exceptions. In [7], the author, Ota and Saito also characterized all those graphs which satisfy the assumption of the conjecture, but are not 1-tough and, by using this, they verified the conjecture for k=1 and 2. In this paper, we verify the conjecture for k=3 and 4.