Abstract 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 other famous properties of graph theory (like chordality, co-comparability, or being unit-interval). 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 determinant ideals). 

This is joint work with Matteo Varbaro, Lisa Seccia.

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