On a Theorem of Sewell and Trotter
Abstract
Sewell and Trotter [J. Combin. Theory Ser. B, 1993] proved that every connected alpha-critical graph that is not isomorphic to K1, K2 or an odd cycle contains a totally odd K4-subdivision. Their theorem implies an interesting min-max relation for stable sets in graphs without totally odd K4-subdivisions. In this note, we give a simpler proof of Sewell and Trotter's theorem.
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