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}
}
Comments
Referee comments incorporated