Coloring with no 2-colored P4's

Michael O. Albertson, Glenn G. Chappell, Henry Kierstead, André Kündgen, Radhika Ramamurthi

Research output: Contribution to journalArticle

84 Scopus citations

Abstract

A proper coloring of the vertices of a graph is called a star coloring if every two color classes induce a star forest. Star colorings are a strengthening of acyclic colorings, i.e., proper colorings in which every two color classes induce a forest. We show that every acyclic k-coloring can be refined to a star coloring with at most (2k2 - k) colors. Similarly, we prove that planar graphs have star colorings with at most 20 colors and we exhibit a planar graph which requires 10 colors. We prove several other structural and topological results for star colorings, such as: cubic graphs are 7-colorable, and planar graphs of girth at least 7 are 9-colorable. We provide a short proof of the result of Fertin, Raspaud, and Reed that graphs with tree-width t can be star colored with (2t+2) colors, and we show that this is best possible.

Original languageEnglish (US)
JournalElectronic Journal of Combinatorics
Volume11
Issue number1 R
DOIs
StatePublished - Mar 31 2004

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics
  • Applied Mathematics

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    Albertson, M. O., Chappell, G. G., Kierstead, H., Kündgen, A., & Ramamurthi, R. (2004). Coloring with no 2-colored P4's. Electronic Journal of Combinatorics, 11(1 R). https://doi.org/10.37236/1779