Speaker : Dr. Kyle F. Jao (Engineer of Yahoo! Inc.) Circular Chromatic Ramsey Number 2014-02-21 (Fri) 14:00 - 15:30 Seminar Room 617, Institute of Mathematics (NTU Campus) We introduce the $\it circular chromatic Ramsey number$ $R_{\chi_c}({\cal F},{\cal G})$ as the infimum of the circular chromatic numbers of graphs $H$ such that every red/blue edge-coloring of $H$ yields a red copy of a graph in $\cal F$ or a blue copy of a graph in $\cal G$. We prove $R_{\chi_c}(K_3,K_3)=6$ and $R_{\chi_c}(K_3,K_4)=9$. Also, if $\cal F$ and $\cal G$ each contain a graph with circular chromatic number at most $5/2$ (such as any odd cycle of length at least $5$), then $R_{\chi_c}({\cal F},{\cal G})=4$. Furthermore, no graph has circular chromatic Ramsey number between $4$ and $5$. Joint work with Claude Tardif, Douglas West, and Xuding Zhu.