Coloring with no 2-colored P 4's

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

Research output: Contribution to journalArticle

82 Citations (Scopus)

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 (2k 2 - 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 ( 2 t+2) colors, and we show that this is best possible.

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

Fingerprint

Coloring
Colouring
Star
Stars
Color
Planar graph
Acyclic Coloring
Treewidth
Cubic Graph
Girth
Strengthening
Graph in graph theory
Vertex of a graph

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

Cite this

Albertson, M. O., Chappell, G. G., Kierstead, H., Kündgen, A., & Ramamurthi, R. (2004). Coloring with no 2-colored P 4's. Electronic Journal of Combinatorics, 11(1 R).

Coloring with no 2-colored P 4's. / Albertson, Michael O.; Chappell, Glenn G.; Kierstead, Henry; Kündgen, André; Ramamurthi, Radhika.

In: Electronic Journal of Combinatorics, Vol. 11, No. 1 R, 31.03.2004.

Research output: Contribution to journalArticle

Albertson, MO, Chappell, GG, Kierstead, H, Kündgen, A & Ramamurthi, R 2004, 'Coloring with no 2-colored P 4's', Electronic Journal of Combinatorics, vol. 11, no. 1 R.
Albertson MO, Chappell GG, Kierstead H, Kündgen A, Ramamurthi R. Coloring with no 2-colored P 4's. Electronic Journal of Combinatorics. 2004 Mar 31;11(1 R).
Albertson, Michael O. ; Chappell, Glenn G. ; Kierstead, Henry ; Kündgen, André ; Ramamurthi, Radhika. / Coloring with no 2-colored P 4's. In: Electronic Journal of Combinatorics. 2004 ; Vol. 11, No. 1 R.
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