“School of Mathematics”
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Paper IPM / M / 16932  


Abstract:  
we show that for every j > 0,
there exists n0 such that for every even n, n > n0, and every graph G with (2+j)n vertices and the minimum degree at least (7/4 + 4j)n, each colouring of the edges of G with three colours results in a monochromatic cycle of length n.
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