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Atlantic Graph Theory Seminar
October 4, 2023 @ 3:30 pm - 4:30 pm
Speaker: Iain Beaton, Acadia University
Title: On the Unimodality of Nearly-Well Dominated Trees
Abstract: A polynomial is said to be unimodal if its coefficients are non-decreasing and then non-increasing. The domination polynomial of a graph G is the generating function of the number of dominating sets of each cardinality in G, and its coefficients have been conjectured to be unimodal. In this talk we will show the domination polynomial of a tree T is unimodal so long as the sizes of the minimal dominating sets of T do not differ by too much. We will also discuss a version of this result for directed trees and its connection to the unimodality conjecture for the independence polynomial of a well-covered tree.