### Abstract

Several new tools are presented for determining the number of cliques needed to (edge-)partition a graph. For a graph on n vertices, the clique partition number can grow end times as fast as the clique covering number, where c is at least 1/64. If in a clique on n vertices, the edges between cn^{a} vertices are deleted,1/2≤a≤1, then the number of cliques needed to partition what is left is asymptotic to c^{2}n^{2a}; this fills in a gap between results of Wallis for a≤1/2 and Pullman and Donald for a=1, c≥1/2. Clique coverings of a clique minus a matching are also investigated.

Original language | English |
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Pages (from-to) | 93-101 |

Number of pages | 9 |

Journal | Annals of Discrete Mathematics |

Volume | 38 |

Issue number | C |

DOIs | |

Publication status | Published - 1988 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics

### Cite this

*Annals of Discrete Mathematics*,

*38*(C), 93-101. https://doi.org/10.1016/S0167-5060(08)70774-X

**Clique Partitions and Clique Coverings.** / Erdős, P.; Faudree, Ralph; Ordman, Edward T.

Research output: Contribution to journal › Article

*Annals of Discrete Mathematics*, vol. 38, no. C, pp. 93-101. https://doi.org/10.1016/S0167-5060(08)70774-X

}

TY - JOUR

T1 - Clique Partitions and Clique Coverings

AU - Erdős, P.

AU - Faudree, Ralph

AU - Ordman, Edward T.

PY - 1988

Y1 - 1988

N2 - Several new tools are presented for determining the number of cliques needed to (edge-)partition a graph. For a graph on n vertices, the clique partition number can grow end times as fast as the clique covering number, where c is at least 1/64. If in a clique on n vertices, the edges between cna vertices are deleted,1/2≤a≤1, then the number of cliques needed to partition what is left is asymptotic to c2n2a; this fills in a gap between results of Wallis for a≤1/2 and Pullman and Donald for a=1, c≥1/2. Clique coverings of a clique minus a matching are also investigated.

AB - Several new tools are presented for determining the number of cliques needed to (edge-)partition a graph. For a graph on n vertices, the clique partition number can grow end times as fast as the clique covering number, where c is at least 1/64. If in a clique on n vertices, the edges between cna vertices are deleted,1/2≤a≤1, then the number of cliques needed to partition what is left is asymptotic to c2n2a; this fills in a gap between results of Wallis for a≤1/2 and Pullman and Donald for a=1, c≥1/2. Clique coverings of a clique minus a matching are also investigated.

UR - http://www.scopus.com/inward/record.url?scp=77957091574&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77957091574&partnerID=8YFLogxK

U2 - 10.1016/S0167-5060(08)70774-X

DO - 10.1016/S0167-5060(08)70774-X

M3 - Article

VL - 38

SP - 93

EP - 101

JO - Annals of Discrete Mathematics

JF - Annals of Discrete Mathematics

SN - 0167-5060

IS - C

ER -