Andrzej Dudek

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20242026

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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

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.CO2024

Generalized Ramsey numbers at the linear and quadratic thresholds

Patrick Bennett, Ryan Cushman, Andrzej Dudek

The generalized Ramsey number $f (n, p, q)$ is the smallest number of colors needed to color the edges of the complete graph $K_{n}$ so that every $p$ -clique spans at least $q$ colors…

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

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

Generalized Ramsey numbers at the linear and quadratic thresholds

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