Alistair Benford

activity

20212026

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3 papers · 1 filter

math.CO2023

Unavoidable structures in infinite tournaments

Alistair Benford, Louis DeBiasio, Paul Larson

We prove a strong dichotomy result for countably-infinite oriented graphs; that is, we prove that for all countably-infinite oriented graphs $G$ , either (i) there is a countably-in…

math.CO2022

Trees with many leaves in tournaments

Alistair Benford, Richard Montgomery

Sumner's universal tournament conjecture states that every $(2 n - 2)$ -vertex tournament should contain a copy of every $n$ -vertex oriented tree. If we know the number of leaves of an…

math.CO2021

Trees with few leaves in tournaments

Alistair Benford, Richard Montgomery

We prove that there exists $C > 0$ such that any $(n + C k)$ -vertex tournament contains a copy of every $n$ -vertex oriented tree with $k$ leaves, improving the previously best known bou…