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For a positive integer t and a graph F, the numbers ERt (F) and V Rt (F) of F are the minimum positive integer n such that every red-blue coloring of the edges of the complete graph Kn results in t pairwise edge-disjoint and vertex-disjoint, respectively, monochromatic copies of F in Kn. The number ERt (F) is determined when F = K3 for t ≤ 4 and when F is the path P3 of order 3 for every positive integer t, while V Rt (F) is determined when F ∈ K3, P3 for every positive integer t.
Chartrand et al. (Wed,) studied this question.