Toughness and (a,b,k)-critical graphs

  • Authors:

  • Sizhong Zhou;Jiashang Jiang

  • Affiliations:

  • School of Mathematics and Physics, Jiangsu University of Science and Technology, Mengxi Road 2, Zhenjiang, Jiangsu 212003, People's Republic of China;School of Mathematics and Physics, Jiangsu University of Science and Technology, Mengxi Road 2, Zhenjiang, Jiangsu 212003, People's Republic of China

  • Venue:
  • Information Processing Letters
  • Year:
  • 2011

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Abstract

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)=+~. In this paper, it is proved that a graph G is an (a,b,k)-critical graph if G satisfies @d(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.