Note on 2-edge-colorings of complete graphs with small monochromatic k-connected subgraphs - Jin, Ze-min; Wang, Yu-ling; Wen, Shi-li (Applied Mathematics-A Journal of Chinese Universities, 2014)
Bollobás and Gyárfás conjectured that for n > 4 ( k − 1) every 2-edge-coloring of K n contains a monochromatic k -connected subgraph with at least n − 2 k + 2 vertices. Liu, et al. proved that the conjecture holds when n ≥ 13 k − 15. In this note, we characterize all the 2-edge-colorings of K n where each monochromatic k -connected subgraph has at most n −2 k +2 vertices for n ≥ 13 k − 15.