Liam Hardiman

collaborators

2 papers

math.CO2021

Counting Hamiltonian Cycles in Dirac Hypergraphs

Asaf Ferber, Liam Hardiman, Adva Mond

For $0 \leq ℓ < k$ , a Hamiltonian $ℓ$ -cycle in a $k$ -uniform hypergraph $H$ is a cyclic ordering of the vertices of $H$ in which the edges are segments of length $k$ and every…

math.CO2021

On subgraphs with degrees of prescribed residues in the random graph

Asaf Ferber, Liam Hardiman, Michael Krivelevich

We show that with high probability the random graph $G_{n, 1/2}$ has an induced subgraph of linear size, all of whose degrees are congruent to $r (mod q)$ for any fixed $r$ and $q\g…