Department of Mathematics, Aula Magna.
Hamiltonian graphs are graphs where one can find a closed walk that touches all vertices exactly once. Equivalently, they are the graphs whose vertices can be labeled from 1 to n so that all of 12, 23, 34, …, n1 feature among the edges. This second definition has the advantage that it can be extended to simplicial complexes of dimension higher than one. Similarly, one can extend to complexes many other famous properties of graph theory (like chordality or being interval) which can be characterized via vertex labelings.
We extend to all dimensions the famous result that all unit-interval 2-connected graphs are Hamiltonian. If time permits, we also discuss how to characterize unit-interval graphs and complexes in algebraic terms (i.e. in terms of Groebner bases of determinantal ideals).
This is joint work with Matteo Varbaro and Lisa Seccia.
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