Note on 2-edge-colorings of complete graphs with small monochromatic k-connected subgraphs

作者:Jin Ze min*; Wang Yu ling; Wen Shi li
来源:Applied Mathematics-A Journal of Chinese Universities Series B, 2014, 29(2): 249-252.
DOI:10.1007/s11766-014-2859-1

摘要

Bollobas and Gyarfas conjectured that for n > 4 (k - 1) every 2-edge-coloring of K (n) contains a monochromatic k-connected subgraph with at least n - 2k + 2 vertices. Liu, et al. proved that the conjecture holds when n a parts per thousand yen 13k - 15. In this note, we characterize all the 2-edge-colorings of K (n) where each monochromatic k-connected subgraph has at most n-2k+2 vertices for n a parts per thousand yen 13k - 15.

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