Monochromatic subgraphs in graphs
Gary Chartrand, Emma Jent, Ping Zhang · Contributions to Mathematics · 2024
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.