Toughness and (a, b, k)-critical graphs
Let a, b, k be nonnegative integers with 2  = a(k + 1). An [a, b]-factor of a graph G is defined as a spanning subgraph F of G such that a  = 2} if G is not complete; otherwise, t(G) = +infinity. In this paper, it is proved that a graph G is an (a, b, k)-critical graph. if G satisfies delta(G) >= a + k and t(G) >= a - 1 + (a-1)(k+1)/b. Furthermore, it is shown that the result in this paper is best possible in some sense. (C) 2011 Elsevier By. All rights reserved.
toughness (a, b, k)-critical graph graph [a, b]-factor combinatorial problems minimum degree