A note on two orthogonal totally C₄-free one-factorizations of complete graphs

2019/06/21 by Adrián Vázquez-Ávila, Vázquez-Ávila, Adrián · 1 citation
Engineering · Mathematics · #graph theory and CDMA systems #math.CO

paper · pdf · doi:10.48550/arxiv.1906.09291

arxiv created 2020/07/17 · arxiv updated 2020/07/20

Abstract

A pair of orthogonal one-factorizations F and G of the complete graph K_n is totally C₄-free, if the union F∪ G, for any F,G\inF\cupG, does not include a cycle of length four. In this note, we prove if q≡3 (mod 4) is a prime power with q≥11, then there is a pair of orthogonal totally C₄-free one-factorizations of K_q+1.

Cited by

• On (1,C₄) one-factorization and two orthogonal (2,C₄) one-factorization of complete graphs

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