Speaker: Ilkyoo Choi (Hankuk University of Foreign Studies)
Title: Odd colorings and proper conflict-free colorings of graphs
Abstract: The following two notions of relaxations of coloring squares of graphs were recently formally introduced by Petruˇsevski and Skrekovski, and by Fabrici, Luˇzar, Rindoˇsov´a, and Sot´ak: An odd c-coloring (resp. proper conflict-free c-coloring) of a graph is a proper c-coloring such that each non-isolated vertex has a color appearing an odd number of times (resp. exactly once) on its neighborhood. Since its appearance on the arXiv in 2022, there has been over 20 papers on these coloring notions. In this talk, we survey some of these results and conjectures, which includes Brooks-type results and strengthening of the Four Color Conjecture, and so on.