About recognizing (&agr; &bgr;) classes of polar graphs
Discrete Mathematics
Achromatic number is NP-complete for cographs and interval graphs
Information Processing Letters
Easy problems for tree-decomposable graphs
Journal of Algorithms
Complexity of graph partition problems
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Graph classes: a survey
Modular decomposition and transitive orientation
Discrete Mathematics - Special issue on partial ordered sets
Approximating minimum cocolorings
Information Processing Letters
Discrete Applied Mathematics
Discrete Applied Mathematics
Combinatorial Algorithms
A forbidden subgraph characterization of line-polar bipartite graphs
Discrete Applied Mathematics
Recognizing line-polar bipartite graphs in time O(n)
Discrete Applied Mathematics
Algorithms for unipolar and generalized split graphs
Discrete Applied Mathematics
| Hi-index | 0.00 |
Polar graphs generalise bipartite graphs, cobipartite graphs, and split graphs, and they constitute a special type of matrix partitions. A graph is polar if its vertex set can be partitioned into two, such that one part induces a complete multipartite graph and the other part induces a disjoint union of complete graphs. Deciding whether a given arbitrary graph is polar, is an NP-complete problem. Here, we show that for permutation graphs this problem can be solved in polynomial time. The result is surprising, as related problems like achromatic number and cochromatic number are NP-complete on permutation graphs. We give a polynomial-time algorithm for recognising graphs that are both permutation and polar. Prior to our result, polarity has been resolved only for chordal graphs and cographs.