Title: Trees and Subtrees
Speaker: Professor Gary Gordon, Lafayette College
Abstract: Choose a subtree of a complete graph. What is the probability that your subtree is a spanning tree? This question has a very nice answer, and leads to related questions about subtree density (the average size of a subtree) in other graph families. We give examples where adding an edge to a graph decreases the subtree density, and conjecture that for any non-complete graph, there is an edge that can be added that increases this density. We also give a procedure for creating examples of non-isomorphic trees with the same subtree data, i.e., the same number of subtrees having k edges and m leaves for all k and m.
Bio of speaker: Gary Gordon is the Marshall R. Metzgar Professor of Mathematics at Lafayette College, where he’s been teaching since 1986. His research interests include combinatorics and finite geometry, but he likes math problems of all kinds. He served as the editor for The Playground, the problem solving column of Math Horizons, and he is also involved with the AMC10-12 contest. He has won multiple awards from the Math Association of America (MAA), and has co-authored two books. His favorite mathematical activity – writing The Joy of SET about the math behind the card game SET, with co-authors Liz McMahon, Hannah Gordon, and Rebecca Gordon, his wife and two daughters.
Topic: Colloquium lectures
Time: Mar 25, 2022 04:00 PM Central Time (US and Canada)
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