David Galvin

activity

20232025

collaborators

3 papers

math.CO2025

Hoffman-London graphs: When paths minimize $H$ -colorings among trees

David Galvin, Phillip Marmorino, Emily McMillon +2

Given a graph $G$ and a target graph $H$ , an $H$ -coloring of $G$ is an adjacency-preserving vertex map from $G$ to $H$ . The number of $H$ -colorings of $G$ , $hom (G, H)$ , has been st…

math.CO2024

Counting independent sets in regular graphs with bounded independence number

David Galvin, Phillip Marmorino

An $n$ -vertex, $d$ -regular graph can have at most $2^{n /2 + o_{d} (n)}$ independent sets. In this paper we address what happens with this upper bound when we impose the further conditio…

math.CO2023

Factoring complete graphs and hypergraphs into factors with few maximal cliques

Paul Erdős, David P. Galvin, Fred Galvin +1

For integers $r, t \geq 2$ and $n \geq 1$ let $f_{r} (t, n)$ be the minimum, over all factorizations of the complete $r$ -uniform hypergraph of order $n$ into $t$ factors $H_{1}, \dots, H_{t}$ , of…

Hoffman-London graphs: When paths minimize H-colorings among trees

Counting independent sets in regular graphs with bounded independence number

Factoring complete graphs and hypergraphs into factors with few maximal cliques

Hoffman-London graphs: When paths minimize $H$ -colorings among trees