Edge Colourings of Graphs Avoiding Monochromatic Matchings of a Given Size
2012 ◽
Vol 21
(1-2)
◽
pp. 203-218
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Let k and ℓ be positive integers. With a graph G, we associate the quantity ck,ℓ(G), the number of k-colourings of the edge set of G with no monochromatic matching of size ℓ. Consider the function ck,ℓ: given by ck,ℓ(n) = max {ck,ℓ(G): |V(G)| = n}, the maximum of ck,ℓ(G) over all graphs G on n vertices. In this paper, we determine ck,ℓ(n) and the corresponding extremal graphs for all large n and all fixed values of k and ℓ.
2005 ◽
Vol 42
(3)
◽
pp. 277-294
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