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
On the Queue Number of Planar Graphs
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Random Structures & Algorithms
Acyclically 3-colorable planar graphs
WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation
Acyclic colorings of graph subdivisions
IWOCA'11 Proceedings of the 22nd international conference on Combinatorial Algorithms
Acyclic coloring with few division vertices
Journal of Discrete Algorithms
| Hi-index | 0.00 |
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 3-colorable, where the number of division vertices is at most 2.75n-6. This upper bound on the number of division vertices reduces to 2n-6 in the case of acyclic 4-coloring. We show that it is NP-complete to decide whether a graph with degree at most 6 is acyclically 4-colorable or not. Furthermore, we give some upper bounds on the number of division vertices for acyclic 3-coloring of subdivisions of k-trees and cubic graphs.