Note on Highly Connected Monochromatic Subgraphs in 2-Colored Complete Graphs

In this note, 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 ≥ 6.5(k − 1), then in any 2-coloring of the edges of Kn, 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.