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Keywords:

  • graph decompositions;
  • monochromatic graph decomposiitons

Abstract

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 inline image be the smallest number ϕ 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 ϕ parts. Here, we study the function inline image for inline image and inline image.