An upper bound for a ramsey type problem for k-connected subgraphs

For any positive integer k , let r 2 ( k ) denote the smallest integer n such that every 2-edge-colored complete graph K n contains a monochromatic k -connected subgraph. Matula established the bound 4 ( k - 1 ) + 1 ≤ r 2 ( k ) < ( 3 + 11 / 3 ) ( k - 1 ) + 1 . It is known that r 2 ( k ) = 4 ( k -...

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