Higher chordality: From graphs to complexes

TL;DR

This paper extends the concept of chordality from graphs to higher-dimensional simplicial complexes, connecting it with homology theory and generalizing classical graph results.

Contribution

It introduces a homology-based framework for higher-dimensional chordality and generalizes key classical theorems from graph theory to simplicial complexes.

Findings

Established a homology-theoretic definition of higher chordality

Generalized Dirac's chordality theorems to complexes

Linked higher chordality with the Leray property

Abstract

We generalize the fundamental graph-theoretic notion of chordality for higher dimensional simplicial complexes by putting it into a proper context within homology theory. We generalize some of the classical results of graph chordality to this generality, including the fundamental relation to the Leray property and chordality theorems of Dirac.