## Algebra and Combinatorics Seminar

**Date: ** April 5, 2024

**Time: ** 3:00PM - 3:50PM

**Location: ** BLOC 302

**Speaker: **Chun-Hung Liu, TAMU

**Title: ***Asymptotically optimal proper conflict-free coloring of bounded maximum degree graphs*

**Abstract: **Every graph of maximum degree d has a coloring with d+1 colors such that no two adjacent vertices receive the same color. Caro, Petrusevski, Skrekovski conjectured that if d >2, then one can always choose such a proper (d+1)-coloring such that for every non-isolated vertex, some color appears on its neighborhood exactly once. We prove that this conjecture holds asymptotically: every graph of maximum degree d has a proper coloring with (1+o(1))d colors such that for every non-isolated vertex, some color appears on its neighborhood exactly once. Joint work with Bruce Reed.