Monochromatic partitions in 2-edge-coloured bipartite graphs
Résumé
We study two variations of the Gyarfas--Lehel conjecture on the minimum number of monochromatic components needed to cover an edge-coloured complete bipartite graph. Specifically, we show the following.
- For p>> (\log n/n)^{1/2}, w.h.p.~every 2-colouring of the random bipartite graph G~ G(n,n,p) admits a cover of all but O(1/p) vertices of G using at most three vertex-disjoint monochromatic components.
- For every 2-colouring of a bipartite graph G with parts of size n and minimum degree (13/16+o(1))n, the vertices of G can be covered using at most three vertex-disjoint monochromatic components.
Domaines
Combinatoire [math.CO]
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Monochromatic_Partitions_in_2-edge-coloured_Bipartite_Graphs.pdf (335.49 Ko)
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