Acyclically 3-colorable planar graphs

Authors:
Patrizio Angelini;Fabrizio Frati
Affiliations:
Dipartimento di Informatica e Automazione, Roma Tre University;Dipartimento di Informatica e Automazione, Roma Tre University
Venue:
WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation
Year:
2010

Citing 4
Cited 3

Efficiently four-coloring planar graphs

STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Total colourings of planar graphs with large girth

European Journal of Combinatorics
Acyclic colorings of subcubic graphs

Information Processing Letters
Acyclic coloring of graphs

Random Structures & Algorithms

Acyclic colorings of graph subdivisions

IWOCA'11 Proceedings of the 22nd international conference on Combinatorial Algorithms
Acyclically 3-colorable planar graphs

Journal of Combinatorial Optimization
Acyclic colorings of graph subdivisions revisited

Journal of Discrete Algorithms

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper we study the planar graphs that admit an acyclic 3-coloring. We show that testing acyclic 3-colorability is $\cal NP$-hard for planar graphs of maximum degree 4 and we show that there exist infinite classes of cubic planar graphs that are not acyclically 3-colorable. Further, we show that every planar graph has a subdivision with one vertex per edge that is acyclically 3-colorable. Finally, we characterize the series-parallel graphs such that every 3-coloring is acyclic and we provide a linear-time recognition algorithm for such graphs.