Commit da742c6b authored by lbcric79's avatar lbcric79

ajout resume Hendrik

parent 5be83916
Title: Polygon contact representations
date: 2020-05-06 10:30
slug: 2020-05-06-combi-seminaire
Authors: Hendrik Schrezenmaier
institution: TU Berlin
tags: Combi seminar, combinatorics
location: à distance
En ligne
In a contact representation of a planar graph, the vertices of
the graph are represented by objects in the plane with disjoint
interiors and the edges correspond to touchings of these objects. The
combinatorics of contact representations of planar triangulations with
homothetic triangles are known to be described by Schnyder woods and the
combinatorics of contact representations with axis-aligned rectangles
are known to be described by transversal structures. In this talk, we
will introduce a generalization of these structures that is suitable to
describe the combinatorics of contact representations with regular
K-gons for arbitrary K>=5.
Afterwards, we will see how these structures can be used for the
computation of the contact representations and for proving their
existence. The idea of these methods is to associate a system of linear
equations with each K-contact structure and to search for a K-contact
structure whose system of equations has a non-negative solution. Then
this solution encodes the contact representation. The way this search is
done is quite beautiful and produces nice pictures.
This is joint work with Stefan Felsner and Raphael Steiner.
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