English

On a Theorem of Sewell and Trotter

Combinatorics 2008-12-15 v2

Abstract

Sewell and Trotter [J. Combin. Theory Ser. B, 1993] proved that every connected alpha-critical graph that is not isomorphic to K_1, K_2 or an odd cycle contains a totally odd K_4-subdivision. Their theorem implies an interesting min-max relation for stable sets in graphs without totally odd K_4-subdivisions. In this note, we give a simpler proof of Sewell and Trotter's theorem.

Keywords

Cite

@article{arxiv.0712.3956,
  title  = {On a Theorem of Sewell and Trotter},
  author = {Samuel Fiorini and Gwenaël Joret},
  journal= {arXiv preprint arXiv:0712.3956},
  year   = {2008}
}

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