## Abstract

A set of pairwise edge-disjoint triangles of an edge-colored K_{n} is r-color avoiding if it does not contain r monochromatic triangles, each having a different color. Let f_{r}(n) be themaximum integer so that in every edge coloring of K_{n} with r colors, there is a set of f _{r}(n) pairwise edge-disjoint triangles that is r-color avoiding. We prove that 0.1177n^{2}(1 - o(1)) < f2(n) < 0.1424n^{2}(1 + o(1)). The proof of the lower bound uses probabilistic arguments, fractional relaxation and some packing theorems. We also prove that f_{r}(n)/n ^{2} < 1/6 (1 - 0.145^{r-1}) + o(1). In particular, for every r, if n is sufficiently large, there are edge colorings of K_{n} with r colors so that the removal of any o(n^{2}) members from any Steiner triple system does not turn it r-color avoiding.

Original language | English |
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Pages (from-to) | 195-204 |

Number of pages | 10 |

Journal | SIAM Journal on Discrete Mathematics |

Volume | 23 |

Issue number | 1 |

DOIs | |

State | Published - 2008 |

## Keywords

- Edge coloring
- Packing
- Triangles

## ASJC Scopus subject areas

- General Mathematics