Louis DeBiasio

collaborators

8 papers

math.CO2026

The Hajnal-Szemerédi theorem in digraphs revisited

Louis DeBiasio, Hal Kierstead

Treglown conjectured (in a complementary form) that for every positive integer $k$ , every digraph $D$ satisfying $min {d^{+} (v), d^{-} (v)} \leq k - 1$ for all $v \in V (D)$ has an equitable…

math.CO2026

On the Ramsey numbers of wheels, cycles, and stars

Louis DeBiasio, Tucker Wimbish

The wheel $W_{k}$ is the graph on $k + 1$ vertices consisting of a vertex joined to a cycle of length $k$ , and we say that $W_{k}$ is an even wheel if $k$ is even. Mao, Wang, Magnant,…

math.CO2026

A note on the multicolor size-Ramsey numbers of connected graphs

Louis DeBiasio

The $r$ -color size-Ramsey number of a graph $H$ , denoted by $R_{r} (H)$ , is the minimum number of edges in a graph $G$ having the property that every $r$ -coloring of the edg…

math.CO2026

On the Ramsey numbers of fans and stars

Louis DeBiasio, Tucker Wimbish

Let $F_{n}$ be the graph on $2 n + 1$ vertices consisting of $n$ triangles meeting at a single vertex. After a number of improvements over the years, it is currently known that the Rams…

math.CO2025

Powers of Hamilton cycles in oriented and directed graphs

Louis DeBiasio, Jie Han, Allan Lo +3

The PÃ³sa--Seymour conjecture determines the minimum degree threshold for forcing the $k$ th power of a Hamilton cycle in a graph. After numerous partial results, KomlÃ³s, SÃ¡rkÃ¶zy…

math.CO2025

Arbitrary orientations of Hamilton cycles in directed graphs of large minimum degree

Louis DeBiasio, Andrew Treglown

In 1960, Ghouila-Houri proved that every strongly connected directed graph $G$ on $n$ vertices with minimum degree at least $n$ contains a directed Hamilton cycle. We asymptoticall…