Long monochromatic even cycles in 3-edge-coloured graphs of large\n minimum degree

2020/01/02 by Tomasz Łuczak, Łuczak, Tomasz, Zahra Rahimi +1
Computer Science · Engineering · Mathematics · #05C38 (Secondary) #05C55 (Primary) #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2001.00643

openalex publication_date 2020/01/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that for every \η>0, there exists n₀ such that for every even\nn, n\≥ n₀, and every graph G with (2+\η)n vertices and minimum\ndegree at least (7/4+4\η)n, each colouring of the edges of G with three\ncolours results in a monochromatic cycle of length n.\n

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