 New York Combinatorics Seminar Sponsored by the Graduate Center's Math Department and Computer Science Department Fridays 11:45 am - 12:45 am in Room 4422 This seminar covers a wide range of topics in combinatorics and its applications. The CUNY Graduate Center is located at 365 Fifth Avenue (at the corner of 34th Street), New York. It can be easily reached by subway using the B,D,F,N,Q,R, or 6 train. Seminar Co-Organizers: CUNY: Nadia Benakli (City Tech) Ezra Halleck (City Tech), Sandra Kingan (Brooklyn College), Joseph Malkevitch (York College), Kerry Ojakian (BCC), Mingxian Zhong (Lehman College), Montclair State University: Deepak Bal, Jonathan Cutler Hofstra University: Kira Adaricheva, Eric Rowland Fall 2019 Talks Please note the new room number: 4422 Sep 20, 2019: Kerry Ojakian (BMCC, CUNY) Title: Bounding the k-rainbow total domination number Abstract: A k-rainbow dominating function of a graph G is the following: a function f which assigns a subset of [k] = {1,2,…, k} to each vertex of G, such that if a vertex v is assigned the empty set, then the values assigned to v's neighbors union to [k]. A k-rainbow *total* dominating function is a function f which satisfies the following additional condition: if a vertex is assigned a singleton set {i} then for some neighbor u, we have i in f(u). In either case, the weight of f is the sum of |f(v)| as v ranges over the vertices of G. For a graph G, the k-rainbow domination number is defined as the minimum weight k-rainbow dominating function for G, and the k-rainbow *total* domination number is defined as the minimum weight k-rainbow total dominating function for G. I will present bounds on the rainbow total domination number in terms of the usual domination number, the total domination number, the rainbow domination number and the rainbow total domination number. Along with a number of partial results, I will present questions and conjectures, including a Vizing-like conjecture about graph products for the rainbow total domination number. Previous Co-Organizers Christopher Hanusa (Spring 2011 - Spring 2015) Previous Speakers