Acyclic colorings of graph subdivisions

Authors:
Debajyoti Mondal;Rahnuma Islam Nishat;Sue Whitesides;Md. Saidur Rahman
Affiliations:
Department of Computer Science, University of Manitoba, Canada;Department of Computer Science, University of Victoria, Canada;Department of Computer Science, University of Victoria, Canada;Department of Computer Science and Engineering, Bangladesh University of Engineering and Technology (BUET), Bangladesh
Venue:
IWOCA'11 Proceedings of the 22nd international conference on Combinatorial Algorithms
Year:
2011

Citing 6
Cited 2

The cyclic coloring problem and estimation of spare hessian matrices

SIAM Journal on Algebraic and Discrete Methods
Acyclic colorings of subcubic graphs

Information Processing Letters
Layout of Graphs with Bounded Tree-Width

SIAM Journal on Computing
Efficient Computation of Sparse Hessians Using Coloring and Automatic Differentiation

INFORMS Journal on Computing
Greedy Drawings of Triangulations

Discrete & Computational Geometry
Acyclically 3-colorable planar graphs

WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation

Acyclic colorings of graph subdivisions revisited

Journal of Discrete Algorithms
Acyclic coloring with few division vertices

Journal of Discrete Algorithms

Quantified Score

Hi-index	0.00

Visualization

Abstract

An acyclic coloring of a graph G is a coloring of the vertices of G, where no two adjacent vertices of G receive the same color and no cycle of G is bichromatic. An acyclic k-coloring of G is an acyclic coloring of G using at most k colors. In this paper we prove that any triangulated plane graph G with n vertices has a subdivision that is acyclically 4-colorable, where the number of division vertices is at most 2n−6. We show that it is NP-complete to decide whether a graph with degree at most 7 is acyclically 4-colorable or not. Furthermore, we give some sufficient conditions on the number of division vertices for acyclic 3-coloring of subdivisions of partial k-trees and cubic graphs.