5 papers · 1 filter
Independent set sequence of some linear hypertrees
David Galvin, Courtney Sharpe
The independent set sequence of trees has been well studied, with much effort devoted to the (still open) question of Alavi, Malde, Schwenk and ErdÅs on whether the independent se…
Trees with non log-concave independent set sequences
David Galvin
We construct a family of trees with independence numbers going to infinity for which the log-concavity relation for the independent set sequence of a tree in the family fails a…
Long paths need not minimize -colorings among trees
David Galvin, Emily McMillon, JD Nir +1
Given a graph and a target graph , an -coloring of is an adjacency-preserving vertex map from to . By appropriate choice of , these colorings can express, f…
Characterizing Graphs as Algebraic Squares
Karen L. Collins, David Galvin, Christine A. Kelley +2
Graphs that are squares under the gluing algebra arise in the study of homomorphism density inequalities such as Sidorenko's conjecture. Recent work has focused on these homomorphi…
The domination polynomial of powers of paths and cycles
David Galvin, Yufei Zhang
A dominating set in a graph is a set of vertices with the property that every vertex in the graph is either in the set or adjacent to something in the set. The domination sequence…