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Number theory seminar
Speaker: K. Mallesham (IIT Bombay)
Title: Spectral theory of automorphic forms
Time, day and date: 11:30:00 AM - 1:00:00 PM, Wednesday, October 16, 2024
Venue: Room 215
Combinatorics seminar
Speaker: Rogers Mathew (IIT Hyderabad)
Title: Extremal results on conflict-free coloring
Time, day and date: 11:30:00 AM - 1:00:00 PM, Wednesday, October 16, 2024
Venue: Ramanujan Hall, Department of Mathematics
Abstract
A conflict-free open neighborhood coloring of a graph is an assignment of colors to the vertices such that for every vertex there is a color that appears exactly once in its open neighborhood. For a graph $G$, the smallest number of colors required for such a coloring is called the conflict-free open neighborhood (CFON) chromatic number and is denoted by $\chi_{ON}(G)$. By considering closed neighborhood instead of open neighborhood, we obtain the analogous notions of conflict-free closed neighborhood
(CFCN) coloring, and CFCN chromatic number (denoted by $\chi_{CN}(G)$). The notion of conflict-free coloring was introduced in 2002, and has since received considerable attention. In this talk, we explore some extremal questions on CFON and CFCN colorings. This talk is based on a joint work with Sriram Bhyravarapu, Shiwali Gupta, and Subrahmanyam Kalyanasundaram.