Short cycles in high genus unicellular maps

no code implementations • 3 Mar 2021 • Svante Janson, Baptiste Louf

We study large uniform random maps with one face whose genus grows linearly with the number of edges, which are a model of discrete hyperbolic geometry.

Probability Combinatorics 05C10, 05C80, 60C05, 60D05

Large expanders in high genus unicellular maps

no code implementations • 23 Feb 2021 • Baptiste Louf

We study large uniform random maps with one face whose genus grows linearly with the number of edges.

Combinatorics Probability 05C10, 05C48, 60C05, 60D05

Finding large expanders in graphs: from topological minors to induced subgraphs

no code implementations • 31 Dec 2020 • Baptiste Louf, Fiona Skerman

Here, we show that the problem of finding a large induced subgraph that is an expander can be reduced to the simpler problem of finding a topological minor that is an expander.

Combinatorics 05C48, 05C83

Planarity and non-separating cycles in uniform high genus quadrangulations

no code implementations • 11 Dec 2020 • Baptiste Louf

We study large uniform random quadrangulations whose genus grow linearly with the number of faces, whose local convergence was recently established by Budzinski and the author arXiv:1902. 00492, arXiv:2012. 05813.

Probability Combinatorics 60D05, 60C05

Local limits of bipartite maps with prescribed face degrees in high genus

no code implementations • 10 Dec 2020 • Thomas Budzinski, Baptiste Louf

We study the local limits of uniform high genus bipartite maps with prescribed face degrees.

Probability Combinatorics 60D05, 60C05, 05A16