Colour-biased Hamilton cycles in random graphs

Lior Gishboliner; Michael Krivelevich; Peleg Michaeli

Colour-biased Hamilton cycles in random graphs

Combinatorics 2021-04-22 v4

Authors: Lior Gishboliner , Michael Krivelevich , Peleg Michaeli

Abstract

We prove that a random graph $G(n,p)$ , with $p$ above the Hamiltonicity threshold, is typically such that for any $r$ -colouring of its edges there exists a Hamilton cycle with at least $(2/(r+ 1)-o(1))n$ edges of the same colour. This estimate is asymptotically optimal.

Keywords

hamilton cycles rainbow coloring graph coloring

Cite

@article{arxiv.2007.12111,
  title  = {Colour-biased Hamilton cycles in random graphs},
  author = {Lior Gishboliner and Michael Krivelevich and Peleg Michaeli},
  journal= {arXiv preprint arXiv:2007.12111},
  year   = {2021}
}

Comments

20 pages, minor corrections

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