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

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...

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Bibliographic Details
Published inApplied 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
LanguageEnglish
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
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Summary: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.
ISSN:1005-1031
1993-0445
DOI:10.1007/s11766-014-2859-1