Improved lower bounds on the number of edges in list critical and online list critical graphs

Henry Kierstead, Landon Rabern

Research output: Contribution to journalArticle


We prove that every k-list-critical graph (k≥7) on n≥k+2 vertices has at least [Formula presented] (k−1+ [Formula presented])n edges where c=(k−3)([Formula presented] − [Formula presented]). This improves the bound established by Kostochka and Stiebitz [11]. The same bound holds for online k-list-critical graphs, improving the bound established by Riasat and Schauz [16]. Both bounds follow from a more general result stating that either a graph has many edges or it has an Alon-Tarsi orientable induced subgraph satisfying a certain degree condition.

Original languageEnglish (US)
JournalJournal of Combinatorial Theory. Series B
Publication statusPublished - Jan 1 2019



  • Critical
  • List coloring
  • Online list coloring

ASJC Scopus subject areas

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

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