On the complexity of recognizing perfectly orderable graphs
Discrete Mathematics
The b-chromatic number of a graph
Discrete Applied Mathematics
Linear-time modular decomposition and efficient transitive orientation of comparability graphs
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On the b-Chromatic Number of Graphs
WG '02 Revised Papers from the 28th International Workshop on Graph-Theoretic Concepts in Computer Science
Improved algorithms for weakly chordal graphs
ACM Transactions on Algorithms (TALG)
Simpler Linear-Time Modular Decomposition Via Recursive Factorizing Permutations
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Graphs and Combinatorics
Colouring of graphs with Ramsey-type forbidden subgraphs
Theoretical Computer Science
List coloring in the absence of two subgraphs
Discrete Applied Mathematics
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A b-coloring is a coloring of the vertices of a graph such that each color class contains a vertex that has a neighbor in all other color classes, and the b-chromatic number of a graph G is the largest integer k such that G admits a b-coloring with k colors. A graph is b-perfect if the b-chromatic number is equal to the chromatic number for every induced subgraph of G. We prove that a graph is b-perfect if and only if it does not contain as an induced subgraph a member of a certain list of 22 graphs. This entails the existence of a polynomial-time recognition algorithm and of a polynomial-time algorithm for coloring exactly the vertices of every b-perfect graph. © 2011 Wiley Periodicals, Inc. J Graph Theory 71:95–122, 2012 © 2012 Wiley Periodicals, Inc.