The priority-based coloring approach to register allocation
ACM Transactions on Programming Languages and Systems (TOPLAS)
On a unique tree representation for P4-extendible graphs
Discrete Applied Mathematics - Special volume: combinatorics and theoretical computer science
P4-laden graphs: a new class of brittle graphs
Information Processing Letters
The b-chromatic number of a graph
Discrete Applied Mathematics
Register allocation by priority-based coloring
SIGPLAN '84 Proceedings of the 1984 SIGPLAN symposium on Compiler construction
On the b-Chromatic Number of Graphs
WG '02 Revised Papers from the 28th International Workshop on Graph-Theoretic Concepts in Computer Science
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Maximum Matchings via Gaussian Elimination
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
On the b-Coloring of Cographs and P 4-Sparse Graphs
Graphs and Combinatorics
Graph b-Coloring for Automatic Recognition of Documents
ICDAR '09 Proceedings of the 2009 10th International Conference on Document Analysis and Recognition
A new clustering approach for symbolic data and its validation: application to the healthcare data
ISMIS'06 Proceedings of the 16th international conference on Foundations of Intelligent Systems
| Hi-index | 0.04 |
A coloring c of a graph G=(V,E) is a b-coloring if in every color class there is a vertex whose neighborhood intersects every other color class. The b-chromatic number of G, denoted @g"b(G), is the greatest integer k such that G admits a b-coloring with k colors. A graph G is tight if it has exactly m(G) vertices of degree m(G)-1, where m(G) is the largest integer m such that G has at least m vertices of degree at least m-1. Determining the b-chromatic number of a tight graph G is NP-hard even for a connected bipartite graph Kratochvil et al. (2002) [18]. In this paper we show that it is also NP-hard for a tight chordal graph. We also show that the b-chromatic number of a split graph can be computed in polynomial time. We then define the b-closure and the partial b-closure of a tight graph, and use these concepts to give a characterization of tight graphs whose b-chromatic number is equal to m(G). This characterization is used to propose polynomial-time algorithms for deciding whether @g"b(G)=m(G) for tight graphs that are complement of bipartite graphs, P"4-sparse and block graphs. We also generalize the concept of pivoted tree introduced by Irving and Manlove (1999) [13] and show its relation with the b-chromatic number of tight graphs.