English

Multicolor Tur\'an numbers

Combinatorics 2021-10-07 v1

Abstract

We consider a natural generalisation of Tur\'an's forbidden subgraph problem and the Ruzsa-Szemer\'edi problem by studying the maximum number exF(n,G)ex_F(n,G) of edge-disjoint copies of a fixed graph FF can be placed on an nn-vertex ground set without forming a subgraph GG whose edges are from different FF-copies. We determine the pairs {F,G}\{F, G\} for which the order of magnitude of exF(n,G)ex_F(n,G) is quadratic and prove several asymptotic results using various tools from the regularity lemma and supersaturation to graph packing results.

Keywords

Cite

@article{arxiv.2110.02367,
  title  = {Multicolor Tur\'an numbers},
  author = {András Imolay and János Karl and Zoltán Lóránt Nagy and Benedek Váli},
  journal= {arXiv preprint arXiv:2110.02367},
  year   = {2021}
}
R2 v1 2026-06-24T06:39:04.430Z