Luke Hawranick

collaborators

2 papers

math.CO2026

Generalized Nordhaus--Gaddum Inequalities for Eigenvalues

Sahil Agarwal, Carter Antley, Joseph Aulenbacher +6

For a graph $G$ , let $λ_{1} (G) \geq λ_{2} (G) \geq \dots \geq λ_{n} (G)$ denote the adjacency eigenvalues of $G$ . We prove that for all looped graphs $G$ on $n$ vertices, \[λ_1(G) + λ_2(\over…

math.CO2026

Covering complete $r$ -partite hypergraphs with few monochromatic components

Luke Hawranick, Ruth Luo

An edge-coloring of a hypergraph is {\em spanning} if every vertex sees every color used in the coloring. In this paper, we prove that for $k \geq 2 r \geq 6$ , in any spanning $k$ -c…

Generalized Nordhaus--Gaddum Inequalities for Eigenvalues

Covering complete r-partite hypergraphs with few monochromatic components

Covering complete $r$ -partite hypergraphs with few monochromatic components