Archdeacon, A.; Froncek, D.; Jajcay, R.; Ryjacek, Z. and Siran, J.
(2003).
*Australasian Journal of Combinatorics*, 27(1) pp. 307–316.

URL: | http://ajc.maths.uq.edu.au/pdf/27/ajc_v27_p307.pdf |
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Google Scholar: | Look up in Google Scholar |

## Abstract

A family of cliques in a graph G is said to be p-regular if any two cliquesin the family intersect in exactly p vertices. A graph G is said to have ap-regular k-clique cover if there is a p-regular family H of k-cliques of Gsuch that each edge of G belongs to a clique in H. Such a p-regular k-clique cover is separable if the complete subgraphs of order p that arise asintersections of pairs of distinct cliques of H are mutually vertex-disjoint.For any given integers p,k,l; p < k, we present bounds on the smallestorder of a graph that has a p-regular k-clique cover with exactly l cliques,and we describe all graphs that have p-regular separable k-clique coverswith l cliques.

Item Type: | Journal Article |
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ISSN: | 1034-4942 |

Academic Unit/Department: | Mathematics, Computing and Technology > Mathematics and Statistics Mathematics, Computing and Technology |

Item ID: | 8090 |

Depositing User: | Jozef Širáň |

Date Deposited: | 14 Jun 2007 |

Last Modified: | 14 Jan 2016 16:32 |

URI: | http://oro.open.ac.uk/id/eprint/8090 |

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