Labelling graphs with a condition at distance 2
SIAM Journal on Discrete Mathematics
Efficiently four-coloring planar graphs
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Zero knowledge and the chromatic number
Journal of Computer and System Sciences - Eleventh annual conference on structure and complexity 1996
On the injective chromatic number of graphs
Discrete Mathematics
Partitioning chordal graphs into independent sets and cliques
Discrete Applied Mathematics - Brazilian symposium on graphs, algorithms and combinatorics
Coloring Powers of Chordal Graphs
SIAM Journal on Discrete Mathematics
List matrix partitions of chordal graphs
Theoretical Computer Science - Graph colorings
The L(h, k)-Labelling Problem: A Survey and Annotated Bibliography
The Computer Journal
Discrete Applied Mathematics
| Hi-index | 0.00 |
We show that one can compute the injective chromatic number of a chordal graph G at least as efficiently as one can compute the chromatic number of (G-B)2, where B are the bridges of G. In particular, it follows that for strongly chordal graphs and so-called power chordal graphs the injective chromatic number can be determined in polynomial time. Moreover, for chordal graphs in general, we show that the decision problem with a fixed number of colours is solvable in polynomial time. On the other hand, we show that computing the injective chromatic number of a chordal graph is NP-hard; and unless NP = ZPP, it is hard to approximate within a factor of n1/3-Ɛ, for any Ɛ 0. For split graphs, this is best possible, since we show that the injective chromatic number of a split graph is 3√n-approximable. (In the process, we correct a result of Agnarsson et al. on inapproximability of the chromatic number of the square of a split graph.).