Speaker: Zimu Xiang (UIUC)
Title: Equitable coloring on semi-planar graphs.
Abstract: Chen, Lih and Wu conjectured that graphs with maximum degree \Delta distinct from K_{\Delta+1} or K_{\Delta,\Delta} when \Delta is odd or odd cycle should admit an equitable \Delta-coloring. For planar graphs, Yap and Zhang confirmed the conjecture with \Delta \ge 13, and Nakprasit confirmed with \Delta \ge 9. We give a proof technique that confirms the conjecture for graphs embeddable into a surface with non-negative Euler characteristic with \Delta \ge 9, which implies the previous result on planar graphs, and using the same technique, we confirm the conjecture for planar graphs with \Delta=8. This is joint work with Alexandr Kostochka and Duo Lin.
