### Abstract

Given a graph G, its clique hypergraph C(G) has the same set of vertices as G and the hyperedges correspond to the (inclusionwise) maximal cliques of G. We consider the question of bicolorability of C(G), i.e., whether the vertices of G can be colored with two colors so that no maximal clique is monochromatic. Our two main results say that deciding the bicolorability of C(G) is NP-complete for perfect graphs, but solvable in polynomial time for all planar graphs.

Original language | English |
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Title of host publication | Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms |

Publisher | SIAM |

Pages | 40-41 |

Number of pages | 2 |

Publication status | Published - 2000 |

Event | 11th Annual ACM-SIAM Symposium on Discrete Algorithms - San Francisco, CA, USA Duration: Jan 9 2000 → Jan 11 2000 |

### Other

Other | 11th Annual ACM-SIAM Symposium on Discrete Algorithms |
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City | San Francisco, CA, USA |

Period | 1/9/00 → 1/11/00 |

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### ASJC Scopus subject areas

- Chemical Health and Safety
- Software
- Safety, Risk, Reliability and Quality
- Discrete Mathematics and Combinatorics

### Cite this

*Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms*(pp. 40-41). SIAM.

**On the complexity of bicoloring clique hypergraphs of graphs.** / Kratochvil, J.; Tuza, Z.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms.*SIAM, pp. 40-41, 11th Annual ACM-SIAM Symposium on Discrete Algorithms, San Francisco, CA, USA, 1/9/00.

}

TY - GEN

T1 - On the complexity of bicoloring clique hypergraphs of graphs

AU - Kratochvil, J.

AU - Tuza, Z.

PY - 2000

Y1 - 2000

N2 - Given a graph G, its clique hypergraph C(G) has the same set of vertices as G and the hyperedges correspond to the (inclusionwise) maximal cliques of G. We consider the question of bicolorability of C(G), i.e., whether the vertices of G can be colored with two colors so that no maximal clique is monochromatic. Our two main results say that deciding the bicolorability of C(G) is NP-complete for perfect graphs, but solvable in polynomial time for all planar graphs.

AB - Given a graph G, its clique hypergraph C(G) has the same set of vertices as G and the hyperedges correspond to the (inclusionwise) maximal cliques of G. We consider the question of bicolorability of C(G), i.e., whether the vertices of G can be colored with two colors so that no maximal clique is monochromatic. Our two main results say that deciding the bicolorability of C(G) is NP-complete for perfect graphs, but solvable in polynomial time for all planar graphs.

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UR - http://www.scopus.com/inward/citedby.url?scp=0033879194&partnerID=8YFLogxK

M3 - Conference contribution

SP - 40

EP - 41

BT - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

PB - SIAM

ER -