Note on highly connected monochromatic subgraphs in 2-colored complete graphs (Q625377)

Summary: We improve upon some recent results concerning the existence of large monochromatic, highly connected subgraphs in a 2-coloring of a complete graph. In particular, we show that if \(n \geq 6.5(k - 1)\), then in any 2-coloring of the edges of \(K_n\), there exists a monochromatic \(k\)-connected subgraph of order at least \(n - 2(k - 1)\). Our result improves upon several recent results by a variety of authors.