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Covering cycles andk-term degree sums
Authors:Mekkia Kouider  Zbigniew Lonc
Affiliation:(1) Laboratoire de Recherche en Informatique, Université de Paris-Sud, Orsay, France;(2) Institute of Mathematics, Warsaw University of Technology, Warsaw, Poland
Abstract:
We show that if
$$sumlimits_{x in S} {deg _{G^x }  geqslant left| G right|}$$
, for every stable set
$$S subseteq Vleft( G right),left| S right| = k$$
, then the vertex set ofG can be covered withk–1 cycles, edges or vertices. This settles a conjecture by Enomoto, Kaneko and Tuza.
Keywords:05 C 38  05 C 70
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