Extracting List Colorings from Large Independent Sets

Henry Kierstead, Landon Rabern

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We take an application of the Kernel Lemma by Kostochka and Yancey [11] to its logical conclusion. The consequence is a sort of magical way to draw conclusions about list coloring (and online list coloring) just from the existence of an independent set incident to many edges. We use this to prove an Ore-degree version of Brooks' Theorem for online list-coloring. The Ore-degree of an edge xy in a graph G is θ(xy). The Ore-degree of G is θ(G) = maxxy∈E(G) θ(xy). We show that every graph with θ ≥ 18 and ω ≤ θ/2 is online (Formula presented.) -choosable. In addition, we prove an upper bound for online list-coloring triangle-free graphs: (Formula presented.). Finally, we characterize Gallai trees as the connected graphs G with no independent set incident to at least ǀGǀ edges.

Original languageEnglish (US)
Pages (from-to)315-328
Number of pages14
JournalJournal of Graph Theory
Issue number3
StatePublished - Nov 2017


  • coloring
  • kernel lemma

ASJC Scopus subject areas

  • Geometry and Topology


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