Mark Budden

activity

20102026

most citedConstructive Methods in Gallai-Ramsey Theory for Hypergraphs

5 citations · 10 across the 9 of their papers we have counts for

collaborators

9 papers

math.CO2026

Weakened Gallai-Ramsey Numbers for Books

Mark Budden, Adam Gregory

For $1 \leq s < t$ and any graph $G$ , the weakened Gallai-Ramsey number $g r_{s}^{t} (G)$ is defined to be the least $p \in N$ such that every Gallai $t$ -coloring of the edges of $K_…

math.CO2026

Gallai-Ramsey Numbers for $ℓ$ -Connected Graphs

Zhao Wang, Lanyanni Zhang, Meiqin Wei +1

Given a nonempty graph $G$ , a collection of nonempty graphs $H$ , and a positive integer $k$ , the Gallai-Ramsey number $gr_{k} (G : H)$ is defined to be the mini…

math.CO2024

Lower Bounds for Multicolor Star-Critical Ramsey Numbers

Mark Budden, Yash Shamsundar Khobragade, Siddhartha Sarkar

The star-critical Ramsey number is a refinement of the concept of a Ramsey number. In this paper, we give equivalent criteria for which the star-critical Ramsey number vanishes. Ne…

math.CO2024

Rainbow Numbers for the Generalized Schur Equation $x_{1} + x_{2} + \dots + x_{m - 1} = x_{m}$

Mark Budden, Bruce Landman

We consider the rainbow Schur number $R S_{m} (n)$ , defined to be the minimum number of colors such that every coloring of ${1, 2, \dots, n}$ , using all $R S_{m} (n)$ colors, contains a ra…

math.CO2020

Algebraic Properties of a Hypergraph Lifting Map

Mark Budden, Josh Hiller, Tommy Meek +1

Recent work in hypergraph Ramsey theory has involved the introduction of a "lifting map" that associates a certain $3$ -uniform hypergraph to a given graph, bounding cliques in a pr…

math.CO2019★ 5 cited

Constructive Methods in Gallai-Ramsey Theory for Hypergraphs

Mark Budden, Joshua Hiller, Andrew Penland

Much recent progress in hypergraph Ramsey theory has focused on constructions that lead to lower bounds for the corresponding Ramsey numbers. In this paper, we consider application…