Remarks on a conjecture of Barat and Toth
R. B. Richter, A. G. Luiz
ARTIGO
Inglês
Agradecimentos: Natural Sciences and Engineering Research Council of Canada. We are grateful to Gordon Royle for his insights and computerskills. We also appreciatethe suggestions from the referees to improve the presentation
In 2010, Barat and Toth verified that any r-critical graph with at most r + 4 vertices has a subdivision of K-r. Based in this result, the authors conjectured that, for every positive integer c, there exists a bound r(c) such that for any r, where r >= r(c), any r-critical graph on r + c vertices...
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In 2010, Barat and Toth verified that any r-critical graph with at most r + 4 vertices has a subdivision of K-r. Based in this result, the authors conjectured that, for every positive integer c, there exists a bound r(c) such that for any r, where r >= r(c), any r-critical graph on r + c vertices has a subdivision of K-r. In this note, we verify the validity of this conjecture for c = 5, and show counterexamples for all c >= 6
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Remarks on a conjecture of Barat and Toth
R. B. Richter, A. G. Luiz
Remarks on a conjecture of Barat and Toth
R. B. Richter, A. G. Luiz
Fontes
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The Electronic Journal of Combinatorics (Fonte avulsa) |