Monochromatic K_r-Decompositions of Graphs

Liu, H., and Teresa Sousa. "Monochromatic K_r-Decompositions of Graphs." Journal of Graph Theory. 76 (2014): 89-100.


Given graphs G and H, and a coloring of the edges of G with k colors, a monochromatic H-decomposition of G is a partition of the edge set of G such that each part is either a single edge or forms a monochromatic graph isomorphic to H. Let f_{k}(n,H) be the smallest number t such that any graph G of order n and any coloring of its edges with k colors, admits a monochromatic H-decomposition with at most t parts. Here we study the function f_{k}(n,K_r) for k≥ 2 and r≥ 3.

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