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On a Theorem of Sewell and Trotter
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.Comment: Referee comments incorporate
Claw-free t-perfect graphs can be recognised in polynomial time
A graph is called t-perfect if its stable set polytope is defined by
non-negativity, edge and odd-cycle inequalities. We show that it can be decided
in polynomial time whether a given claw-free graph is t-perfect
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