Highly connected monochromatic subgraphs

نویسندگان

Béla Bollobás

András Gyárfás

چکیده

We conjecture that for n> 4(k−1) every 2-coloring of the edges of the complete graphKn contains a k-connectedmonochromatic subgraph with at least n − 2(k − 1) vertices. This conjecture, if true, is best possible. Here we prove it for k = 2, and show how to reduce it to the case n< 7k − 6. We prove the following result as well: for n> 16k every 2-colored Kn contains a k-connected monochromatic subgraph with at least n− 12k vertices. © 2007 Elsevier B.V. All rights reserved.

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