Complete-factors and (g,f)-factors

  • Authors:

  • Jianxiang Li;Yinghong Ma

  • Affiliations:

  • Department of Mathematics, Xiangtan Polytechnic University, Xiangtan, Hunan 411201, People's Republic of China;Department of Mathematics, Shandong University, Shandong 250100, People's Republic of China

  • Venue:
  • Discrete Mathematics
  • Year:
  • 2003

Quantified Score

Hi-index 0.05

Visualization

Abstract

A factor F of a graph is called a complete-factor if each component of F is complete. Let G be a graph, F be a complete-factor of G with ω(F) ≥ 2 and f, g be two integer-valued functions defined on V(G) with f(x) ≥ g(x) for all x ∈ V(G). It is proved that if ω(F) ≡ 0 (mod 2), or f(V(G)) even and f(x) ≡ g(x) (mod 2) for all x ∈ V(G), and if G - V(C) has a (g,f)-factor for each component C of F, then G has a (g,f)-factor. We show that the results in this paper are best possible.