English

A note on two orthogonal totally $C_4$-free one-factorizations of complete graphs

Combinatorics 2020-07-20 v3

Abstract

A pair of orthogonal one-factorizations F\mathcal{F} and G\mathcal{G} of the complete graph KnK_n is totally C4C_4-free, if the union FGF\cup G, for any F,GFGF,G\in\mathcal{F}\cup\mathcal{G}, does not include a cycle of length four. In this note, we prove if q3q\equiv3 (mod 4) is a prime power with q11q\geq11, then there is a pair of orthogonal totally C4C_4-free one-factorizations of Kq+1K_{q+1}.

Keywords

Cite

@article{arxiv.1906.09291,
  title  = {A note on two orthogonal totally $C_4$-free one-factorizations of complete graphs},
  author = {Adrián Vázquez-Ávila},
  journal= {arXiv preprint arXiv:1906.09291},
  year   = {2020}
}