Ryan R. Martin

activity

20242026

collaborators

6 papers

math.CO2026

Ramsey numbers of multiple copies of a graph and the random Ramsey theorem

Andrea Freschi, Ryan R. Martin, Andrew Treglown

A well-known result of Burr, ErdÅs and Spencer [Transactions of the American Mathematical Society, 1975] determines the $2$ -colour Ramsey number for any sufficiently large collect…

math.CO2026

The edit distance of word-representable and comparability graphs

Sergey Kitaev, Ryan R. Martin

In this paper, we establish that the maximum edit distance of an $n$ -vertex graph from the hereditary property of word-representable graphs is $n^{2} /8 - o (n^{2})$ . In addition, we estab…

math.CO2025

B-colorings of planar and outerplanar graphs

Ryan R. Martin, MiklÃ³s RuszinkÃ³, GÃ¡bor N. SÃ¡rkÃ¶zy

A coloring of the edges of a graph $G$ in which every $K_{1, 2}$ is totally multicolored is known as a proper coloring and a coloring of the edges of $G$ in which every $K_{1, 2}$ an…

math.CO2025

Tiling randomly perturbed multipartite graphs

Enrique Gomez-Leos, Ryan R. Martin

A perfect $K_{r}$ -tiling in a graph $G$ is a collection of vertex-disjoint copies of the graph $K_{r}$ in $G$ that covers all vertices of $G$ . In this paper, we prove that the threshol…

math.CO2024

Tiling randomly perturbed bipartite graphs

Enrique Gomez-Leos, Ryan R. Martin

A perfect $H$ -tiling in a graph $G$ is a collection of vertex-disjoint copies of a graph $H$ in $G$ that covers all vertices of $G$ . Motivated by papers of Bush and Zhao and of Bal…

math.CO2024

On the proper rainbow saturation numbers of cliques, paths, and odd cycles

Dustin Baker, Enrique Gomez-Leos, Anastasia Halfpap +7

Given a graph $H$ , we say a graph $G$ is properly rainbow $H$ -saturated if there is a proper edge-coloring of $G$ which contains no rainbow copy of $H$ , but adding any edge to $G$ …