Corrigendum to “Even pairs and prism corners in square-free Berge graphs” [J. Combin. Theory, Ser. B 131 (2018) 12–39] (Journal of Combinatorial Theory, Series B (2018) 131 (12–39), (S0095895618300030) (10.1016/j.jctb.2018.01.003))

Maria Chudnovsky, Frédéric Maffray, Paul Seymour, Sophie Spirkl

Research output: Contribution to journalComment/debate

Abstract

The authors regret that the main theorem of the paper (1.6) is not correct as stated. This is due to a mistake in one of the theorems of [1], that has since been corrected, but added another possible outcome that we need to handle. The present proof of 1.6 requires an additional assumption, and shows the following Theorem If G is a square-free flat graph, such that no prism of G has a rung of length one, then either G is a complete graph, or G has an even pair. The additional assumption here is that no prism of G has a rung of length one. This assumption can probably be removed, at the cost of making the proof technically much more difficult, but the authors have not been able to do so yet. The authors would like to apologize for any inconvenience caused.

Original languageEnglish (US)
Pages (from-to)259-260
Number of pages2
JournalJournal of Combinatorial Theory. Series B
Volume133
DOIs
StatePublished - Nov 2018

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

Keywords

  • Eeven pairs
  • Erratum
  • Perfect graphs
  • Prisms

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