Patrick Arras

activity

20222024

collaborators

3 papers

math.CO2024

Asymptotically Enumerating Independent Sets in Regular $k$ -Partite $k$ -Uniform Hypergraphs

Patrick Arras, Frederik Garbe, Felix Joos

The number of independent sets in regular bipartite expander graphs can be efficiently approximated by expressing it as the partition function of a suitable polymer model and trunc…

math.CO2023

Independent sets in discrete tori of odd sidelength

Patrick Arras, Felix Joos

It is a well known result due to Korshunov and Sapozhenko that the hypercube in $n$ dimensions has $(1 + o (1)) \cdot 2 e \cdot 2^{2^{n - 1}}$ independent sets. Jenssen and Keev…

math.CO2022

Ore- and Pósa-type conditions for partitioning $2$ -edge-coloured graphs into monochromatic cycles

Patrick Arras

In 2019, Letzter confirmed a conjecture of Balogh, Barát, Gerbner, Gyárfás and Sárközy, proving that every large $2$ -edge-coloured graph $G$ on $n$ vertices with minimum degree at…

Asymptotically Enumerating Independent Sets in Regular k-Partite k-Uniform Hypergraphs

Independent sets in discrete tori of odd sidelength

Ore- and Pósa-type conditions for partitioning 2-edge-coloured graphs into monochromatic cycles

Asymptotically Enumerating Independent Sets in Regular $k$ -Partite $k$ -Uniform Hypergraphs

Ore- and Pósa-type conditions for partitioning $2$ -edge-coloured graphs into monochromatic cycles