On a Theorem of Sewell and Trotter

Details On a Theorem of Sewell and Trotter On a Theorem of Sewell and Trotter

2007-12-23

arxiv.org/abs/0712.3956v2

European Journal of Combinatorics, Vol. 30 (2), 2009, pp. 425-428

Mathematics

Combinatorics

Referee comments incorporated

Scientific paper

10.1016/j.ejc.2008.05.002

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.

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