DisCoMath Seminar: Combinatorial Orthogonality and Graphs with q=2
Discrete & Computational Math Seminar (DisCoMath)
Combinatorial Orthogonality and Graphs with q=2
Dr. Brendan Rooney
Assistant Professor
School of Mathematical Sciences, RIT
Abstract:
Two vectors are combinatorially orthogonal if the size of the intersection of their supports is not 1. An n×n symmetric matrix is combinatorially orthogonal if every pair of rows, or columns, is combinatorially orthogonal. Every orthogonal pair of vectors is combinatorially orthogonal, and every orthogonal matrix is combinatorially orthogonal. For a graph G, we give a simple structural condition that guarantees the existence of a combinatorially orthogonal matrix in S(G) (the set of symmetric matrices with the same off-diagonal zero-pattern as the adjacency matrix of G). We will see how this connects with work done by Reid and Thomassen on graphs for which every path of length r is contained in a cycle of length s. Finally we discuss implications for finding q(G), and characterizing graphs with q=2.
Speaker Bio:
Dr. Rooney is an Assistant Professor in the School of Mathematical Sciences at RIT. He completed his Ph.D. in Combinatorics and Optimization at the University of Waterloo, Ontario, Canada. Prior to joining RIT, he was a Visiting Assistant Professor in the Department of Mathematical Sciences at Korea Advanced Institute of Science and Technology (KAIST) for three years. Dr. Rooney’s research interests include Graph Theory, Combinatorics and Combinatorial Optimization.
Intended Audience:
Undergraduates, graduates, and experts. Those with interest in the topic.
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