Generalizing the Ramsey Problem through Diameter

  title={Generalizing the Ramsey Problem through Diameter},
  author={Dhruv Mubayi},
  journal={Electron. J. Comb.},
  • D. Mubayi
  • Published 13 November 2001
  • Mathematics, Computer Science
  • Electron. J. Comb.
Given a graph $G$ and positive integers $d,k$, let $f_d^k(G)$ be the maximum $t$ such that every $k$-coloring of $E(G)$ yields a monochromatic subgraph with diameter at most $d$ on at least $t$ vertices. Determining $f_1^k(K_n)$ is equivalent to determining classical Ramsey numbers for multicolorings. Our results include $\bullet$ determining $f_d^k(K_{a,b})$ within 1 for all $d,k,a,b$ $\bullet$ for $d \ge 4$, $f_d^3(K_n)=\lceil n/2 \rceil +1$ or $\lceil n/2 \rceil$ depending on whether $n… 
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