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

• Published in: Applied Mathematics-A Journal of Chinese Universities Vol. 29; no. 2; pp. 249 - 252
• Main Authors: Jin, Ze-min, Wang, Yu-ling, Wen, Shi-li
• Format: Journal Article
• Language: English
• Published: Heidelberg Editorial Committee of Applied Mathematics - A Journal of Chinese Universities 01.06.2014
• Subjects: Applications of Mathematics; Mathematics; Mathematics and Statistics; monochromatic subgraph; connected subgraph; 2-edge-coloring; 05C35; 05C15

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 w...