Local colourings and monochromatic partitions in complete bipartite graphs
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2017Metadata
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Lang, Richard
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Local colourings and monochromatic partitions in complete bipartite graphs
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Abstract
We show that for any 2-local colouring of the edges of the balanced complete bipartite graph Kn,n, its vertices can be covered with at most 3 disjoint monochromatic paths. And, we can cover almost all vertices of any complete or balanced complete bipartite r-locally coloured graph with O(r2) disjoint monochromatic cycles. We also determine the 2-local bipartite Ramsey number of a path almost exactly: Every 2-local colouring of the edges of Kn,n contains a monochromatic path on n vertices.
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URI: https://repositorio.uchile.cl/handle/2250/168804
DOI: 10.1016/j.ejc.2016.09.003
ISSN: 01956698
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European Journal of Combinatorics 60 (2017) 42–54
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