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10 papers · 1 filter
Zeros of Hook Polynomials and Related Questions
Walter Bridges, William Craig, Amanda Folsom +1
We study the zero set of polynomials built from partition statistics, complementing earlier work in this direction by Boyer, Goh, Parry, and others. In particular, addressing a que…
Leaky Forcing: A New Variation of Zero Forcing
Shannon Dillman, Franklin Kenter
Zero forcing is a one-player game played on a graph. The player chooses some set of vertices to color, then iteratively applies a color change rule: If all but one of a colored ver…
Computing Bounds on Product-Graph Pebbling Numbers
Franklin Kenter, Daphne Skipper, Dan Wilson
Given a distribution of pebbles to the vertices of a graph, a pebbling move removes two pebbles from a single vertex and places a single pebble on an adjacent vertex. The pebbling…
On p-ary Bent Functions and Strongly Regular Graphs
Caroline Grant Melles, David Joyner
Our main result is a generalized Dillon-type theorem, giving graph-theoretic conditions which guarantee that a -ary function in an even number of variables is bent, for a pr…
An Optimization-Based Sum-of-Squares Approach to Vizing's Conjecture
Elisabeth Gaar, Daniel Krenn, Susan Margulies +1
Vizing's conjecture (open since 1968) relates the sizes of dominating sets in two graphs to the size of a dominating set in their Cartesian product graph. In this paper, we formula…
On zeros of the characteristic polynomial of matroids of bounded tree-width
Carolyn Chun, Rhiannon Hall, Criel Merino +1
We develop some basic tools to work with representable matroids of bounded tree-width and use them to prove that, for any prime power and constant , the characteristic polyn…