On a theorem of Sewell and Trotter

Sewell and Trotter proved that every connected αα-critical graph that is not isomorphic to K1,K2K1,K2 or an odd cycle contains a totally odd K4K4-subdivision. Their theorem implies an interesting min–max relation for stable sets in graphs without totally odd K4K4-subdivisions. In this note, we give a simpler proof of Sewell and Trotter’s theorem.