Combinatorics, Algebra, & Topology Seminar
Spring 2020
All talks are from 12001300 in the designated room unless otherwise specified.

Apr20

Anant GodboleEast Tennessee State UniversityTime: 12:00 PM

Apr09

TBDXingting WangHoward UniversityTime: 12:00 PM

Apr02

Cong X. KangTexas A&M University, GalvestonTime: 12:00 PM

Mar16

Violeta VasilevskaUtah Valley UniversityTime: 12:00 PM

Feb13

Pebbling in Powers of PathsGlenn HurlbertVirginia Commonwealth UniversityTime: 12:00 PM
View Abstract
The tpebbling number of a graph G is defined to be the minimum number m so that, from any initial configuration of m pebbles on the vertices of G, it is possible to place at least t pebbles on any specified vertex via pebbling moves. It has been conjectured that the pebbling numbers of pyramidfree chordal graphs can be calculated in polynomial time. The kthpower G(k) of the graph G is obtained from G by adding an edge between any two vertices of distance at most k from each other. The kthpower of the path P_n on n is an important class of pyramidfree chordal graphs, and is a stepping stone to the more general class of kpaths and the still more general class of interval graphs. Pachter, Snevily, and Voxman (1995) calculated π(P_n^(2)), Kim (2004) calculated π(P_n^(3)), and Kim and Kim (2010) calculated π(P_n^(4)). Recently, Alcón and I have calculated π_t(P_n^(k)) for all n, k, and t. The pebbling exponent e_π(G) of a graph G was defined by Pachter, et al., to be the minimum k for which π(G(k)) = n(G(k)). Of course, e_π(G) ≤ diam(G), and Czygrinow, Kierstead, Trotter, and I (2002) proved that almost all graphs G have e_π(G) = 1. Lourdusamy and Mathivanan (2015) proved several results on π_t(Cn2), and I proved (2017) an asymptotically tight formula for e_\pi(C ). Our formula for π_t(P(k)) allows us to to compute e_π(Pn) exactly.

Jan13

Algebraically Defined Graphs in Two and Three DimensionsBrian KronenthalKutztown University
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Abstract: In this talk, we will discuss algebraically defined bipartite graphs. Indeed, let F denote a field, and consider the bipartite graph whose partite sets P and L are copies of F^3 such that (p1, p2, p3) ∈ P and [q1, q2, q3] ∈ L are adjacent if and only if p2 + q2 = p1q1 and p3 + f3 = p1q1^2. This graph has girth eight, and of particular interest is whether it is possible to alter these equations by replacing p1q1 and p1q1^2 with other bivariate polynomials to create a nonisomorphic girth eight graph. In addition to discussing some results related to this question, as well as a twodimensional analogue, we will also explain the connection between algebraically defined graphs and incidence geometry, which partially motivates this line of inquiry.