Covering cycles andk-term degree sums


We show that if\(\sum\limits_{x \in S} {\deg _{G^x } \geqslant \left| G \right|}\), for every stable set\(S \subseteq V\left( G \right),\left| S \right| = k\), then the vertex set ofG can be covered withk−1 cycles, edges or vertices. This settles a conjecture by Enomoto, Kaneko and Tuza.

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Kouider, M., Lonc, Z. Covering cycles andk-term degree sums. Combinatorica 16, 407–412 (1996).

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Mathematics Subject Classification (1991)

  • 05 C 38
  • 05 C 70