Discrete Applied Mathematics Seminar by Ilkyoo Choi: Odd Colorings and Proper Conflict-Free Colorings of Graphs

Speaker: Ilkyoo Choi, professor of mathematics, Hankuk University of Foreign Studies (HUFS), South Korea

 

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 Petruševski and Škrekovski, and by Fabrici, Lužar, Rindošová, and Soták: 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) in its neighborhood. Since its appearance on the arXiv in 2022, there have been over 30 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. 

This is joint work with Eun-Kyung Cho, Boram Park, and Hyemin Kwon.

 

 

Discrete Applied Math Seminar