Notes on fractional (1, f)-odd factors of graphs

  • Authors:

  • Jiguo Yu;Guizhen Liu

  • Affiliations:

  • School of Computer Science, Qufu Normal University, Ri-zhao, Shandong, P.R. China;School of Mathematics and System Science, Ji-nan, Shandong University, Shandong, P.R. China

  • Venue:
  • FAW'07 Proceedings of the 1st annual international conference on Frontiers in algorithmics
  • Year:
  • 2007

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Abstract

Let G be a simple graph and f an odd integer-valued function defined on V (G). A spanning subgraph F of G is called a fractional (1, f)- odd factor if dF (v) ∈ {1, 3, . . . , f(v)} for all v ∈ V (G), where dF (v) is the fractional degree of v in F. In this paper, we discuss the existence for a graph to have a fractional (1, f)-odd-factor. A necessary and sufficient condition for a tree to have a fractional (1, f)-odd factor is given.