### Abstract

Let f (n ; C_{4}) be the smallest integer such that, given any set of edge disjoint quadrilaterals on n vertices, one can extend it into a complete quadrilateral decomposition by including at most f (n ; C_{4}) additional vertices. It is known, and it is easy to show, that sqrt(n) - 1 ≤ f (n ; C_{4}). Here we settle the longstanding problem that f (n ; C_{4}) = sqrt(n) + o (sqrt(n)).

Original language | English |
---|---|

Pages (from-to) | 466-474 |

Number of pages | 9 |

Journal | Journal of Combinatorial Theory, Series A |

Volume | 117 |

Issue number | 4 |

DOIs | |

Publication status | Published - May 2010 |

### Fingerprint

### Keywords

- Graphs
- H-designs
- Packings
- Quadrilaterals

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science
- Computational Theory and Mathematics

### Cite this

*Journal of Combinatorial Theory, Series A*,

*117*(4), 466-474. https://doi.org/10.1016/j.jcta.2009.06.003

**Tight embeddings of partial quadrilateral packings.** / Füredi, Z.; Lehel, Jeno.

Research output: Contribution to journal › Article

*Journal of Combinatorial Theory, Series A*, vol. 117, no. 4, pp. 466-474. https://doi.org/10.1016/j.jcta.2009.06.003

}

TY - JOUR

T1 - Tight embeddings of partial quadrilateral packings

AU - Füredi, Z.

AU - Lehel, Jeno

PY - 2010/5

Y1 - 2010/5

N2 - Let f (n ; C4) be the smallest integer such that, given any set of edge disjoint quadrilaterals on n vertices, one can extend it into a complete quadrilateral decomposition by including at most f (n ; C4) additional vertices. It is known, and it is easy to show, that sqrt(n) - 1 ≤ f (n ; C4). Here we settle the longstanding problem that f (n ; C4) = sqrt(n) + o (sqrt(n)).

AB - Let f (n ; C4) be the smallest integer such that, given any set of edge disjoint quadrilaterals on n vertices, one can extend it into a complete quadrilateral decomposition by including at most f (n ; C4) additional vertices. It is known, and it is easy to show, that sqrt(n) - 1 ≤ f (n ; C4). Here we settle the longstanding problem that f (n ; C4) = sqrt(n) + o (sqrt(n)).

KW - Graphs

KW - H-designs

KW - Packings

KW - Quadrilaterals

UR - http://www.scopus.com/inward/record.url?scp=76349089553&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=76349089553&partnerID=8YFLogxK

U2 - 10.1016/j.jcta.2009.06.003

DO - 10.1016/j.jcta.2009.06.003

M3 - Article

VL - 117

SP - 466

EP - 474

JO - Journal of Combinatorial Theory - Series A

JF - Journal of Combinatorial Theory - Series A

SN - 0097-3165

IS - 4

ER -