Monochromatic Clique Decompositions of Graphs
Let G be a graph whose edges are colored with k colors, and be a k-tuple of graphs. A monochromatic -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 copy of in color i, for some . Let be the smallest number ?, such that, for every order-n graph and every k-edge-coloring, there is a monochromatic -decomposition with at most ? elements. Extending the previous results of Liu and Sousa [Monochromatic -decompositions of graphs, J Graph Theory 76 (2014), 89100], we solve this problem when each graph in is a clique and is sufficiently large.
monochromatic graph decomposition turn number ramsey number