Patrick Bennett

collaborators

4 papers

math.CO2026

Almost-perfect packings and Tuza's conjecture in the random geometric graph

Patrick Bennett, Ryan Cushman, Andrzej Dudek +1

The triangle packing number $I^½ (G)$ of a graph $G$ is the maximum size of a set of edge-disjoint triangles in $G$ . Tuza conjectured that in any graph $G$ there exists a set of at m…

math.CO2025

Edge-coloring $K_{n, n}$ with no 2-colored $C_{2 k}$

Deepak Bal, Patrick Bennett

The generalized Ramsey number $r (G, H, q)$ is the minimum number of colors needed to color the edges of $G$ such that every isomorphic copy of $H$ has at least $q$ colors. In this…

math.CO2025

The generalized Ramsey number $f (n, 5, 8) = \frac{6}{7} n + o (n)$

Patrick Bennett, Ryan Cushman, Andrzej Dudek

A $(p, q)$ -coloring of $K_{n}$ is a coloring of the edges of $K_{n}$ such that every $p$ -clique has at least $q$ distinct colors among its edges. The generalized Ramsey number $f(n, p,…

math.PR2025

Extending Wormald's Differential Equation Method to One-sided Bounds

Patrick Bennett, Calum MacRury

In this note, we formulate a "one-sided" version of Wormald's differential equation method. In the standard "two-sided" method, one is given a family of random variables which evol…

Almost-perfect packings and Tuza's conjecture in the random geometric graph

Edge-coloring Kn,n​ with no 2-colored C2k​

The generalized Ramsey number f(n,5,8)=76​n+o(n)

Extending Wormald's Differential Equation Method to One-sided Bounds

Edge-coloring $K_{n, n}$ with no 2-colored $C_{2 k}$

The generalized Ramsey number $f (n, 5, 8) = \frac{6}{7} n + o (n)$