Monochromatic Connectivity in Monochromatic-Star-Free Graphs
Journal of Combinatorial Mathematics and Combinatorial Computing
We consider edge-colorings of complete graphs in which each color induces a subgraph that does not contain an induced copy of K1,t for some t > 3. It turns out that such colorings, if the underlying graph is sufficiently large, contain spanning monochromatic κ-connected subgraphs. Furthermore, there exists a color, say blue, such that every vertex has very few incident edges in colors other than blue.
Magnant, Colton, Pouria Salehi Nowbandegani.
"Monochromatic Connectivity in Monochromatic-Star-Free Graphs."
Journal of Combinatorial Mathematics and Combinatorial Computing, 99: 89-96.