Patrick Bennett

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20242026

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5 papers · 1 filter

math.CO2026

Expected cost in Combinatorial Optimization under color constraints

Patrick Bennett, Alan Frieze, Wesley Pegden

We present an average case model of classical problems in combinatorial optimization where there are color constraints. In all cases we seek some (spanning) sub-structure of a comp…

math.CO2026

Binomial Random Matroids

Patrick Bennett, Alan Frieze

Let $B = B_{k, n, p}$ be a random collection of $k$ -subsets of $[n]$ where each possible set is present independently with probability $p$ . Let $E_{B}$ …

math.CO2025

On Minimum Cost Rainbow Structures

Patrick Bennett, Quentin Dubroff, Alan Frieze +1

We discuss the expected minimum cost of rainbow spanning trees and Hamilton cycles in randomly edge colored random graphs.

math.CO2025

Some Maker-Breaker games on hypergraphs

Patrick Bennett, Alan Frieze, Wesley Pegden

We consider some biased Maker-Breaker games. Starting with the complete $k$ -uniform hypergraph on $n$ vertices, at each turn Maker claims one edge, and then Breaker claims $b$ edge…

math.CO2024

Patrick Bennett, Alan Frieze, Wesley Pegden

We study the intersection of a random geometric graph with an ErdÅs-RÃ©nyi graph. Specifically, we generate the random geometric graph $G (n, r)$ by choosing $n$ points uniformly a…

Expected cost in Combinatorial Optimization under color constraints

Binomial Random Matroids

On Minimum Cost Rainbow Structures

Some Maker-Breaker games on hypergraphs

The intersection of a random geometric graph with an ErdÅs-RÃ©nyi graph

The intersection of a random geometric graph with an ErdÅs-RÃ©nyi graph