About recognizing (&agr; &bgr;) classes of polar graphs
Discrete Mathematics
Handbook of graph grammars and computing by graph transformation: volume I. foundations
Handbook of graph grammars and computing by graph transformation: volume I. foundations
Complexity of graph partition problems
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Partitioning chordal graphs into independent sets and cliques
Discrete Applied Mathematics - Brazilian symposium on graphs, algorithms and combinatorics
List matrix partitions of chordal graphs
Theoretical Computer Science - Graph colorings
Discrete Applied Mathematics
Complexity of generalized colourings of chordal graphs
Complexity of generalized colourings of chordal graphs
A forbidden subgraph characterization of line-polar bipartite graphs
Discrete Applied Mathematics
On injective colourings of chordal graphs
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Recognizing line-polar bipartite graphs in time O(n)
Discrete Applied Mathematics
Recognizing polar planar graphs using new results for monopolarity
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Polar permutation graphs are polynomial-time recognisable
European Journal of Combinatorics
Graph partitions with prescribed patterns
European Journal of Combinatorics
Algorithms for unipolar and generalized split graphs
Discrete Applied Mathematics
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Polar graphs are a common generalization of bipartite, cobipartite, and split graphs. They are defined by the existence of a certain partition of vertices, which is NP-complete to decide for general graphs. It has been recently proved that for cographs, the existence of such a partition can be characterized by finitely many forbidden subgraphs, and hence tested in polynomial time. In this paper we address the question of polarity of chordal graphs, arguing that this is in essence a question of colourability, and hence chordal graphs are a natural restriction. We observe that there is no finite forbidden subgraph characterization of polarity in chordal graphs; nevertheless we present a polynomial time algorithm for polarity of chordal graphs. We focus on a special case of polarity (called monopolarity) which turns out to be the central concept for our algorithms. For the case of monopolar graphs, we illustrate the structure of all minimal obstructions; it turns out that they can all be described by a certain graph grammar, permitting our monopolarity algorithm to be cast as a certifying algorithm.