Minimum degree conditions for monochromatic cycle partitioning
نویسندگان
چکیده
A classical result of Erd?s, Gyárfás and Pyber states that any r-edge-coloured complete graph has a partition into O(r2log?r) monochromatic cycles. Here we determine the minimum degree threshold for this property. More precisely, show there exists constant c such on n vertices with at least n/2+c?rlog?n O(r2) We also provide constructions showing condition number cycles are essentially tight.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2021
ISSN: ['0095-8956', '1096-0902']
DOI: https://doi.org/10.1016/j.jctb.2020.07.005