List colorings and reducibility

Zs Tuza, M. Voigt

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Let G be a simple graph, L(v) a list of allowed colors assigned to each vertex v of G, and U an arbitrary subset of the vertex set. The graph G is called k-choosable if, for any list assignment with |L(v)| =k for all v ∈ V, it is possible to color all vertices with colors from their lists in a proper way (i.e., no monochromatic edge occurs). We say that G is U-reducible if, for every list assignment of G where all lists have the same number of elements, we can color the vertices of U with colors from their lists such that for every vertex v ∉ U at most one color of L(v) appears in the coloring of those neighbors of v which belong to U. The concept of reducibility is closely related to list colorings and choosability. The main result of this paper states that a bipartite graph G is U-reducible for every set U if and only if G is 2-choosable.

Original languageEnglish
Pages (from-to)247-256
Number of pages10
JournalDiscrete Applied Mathematics
Volume79
Issue number1-3
DOIs
Publication statusPublished - Nov 27 1997

Keywords

  • Choosability
  • Graph
  • List coloring
  • Vertex coloring

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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