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Main Author:	Ghasr, Fahimeh Khosh-Ahang
Format:	Preprint
Published:	2025
Subjects:	Combinatorics Commutative Algebra
Online Access:	https://arxiv.org/abs/2510.16722
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author	Ghasr, Fahimeh Khosh-Ahang
author_facet	Ghasr, Fahimeh Khosh-Ahang
contents	We introduce and investigate generalizations of interval and proper interval graphs to simplicial complexes, including strong interval, unit interval, and under closed variants. Through equivalent combinatorial and algebraic characterizations, we uncover hierarchies among these classes and extend key results to higher dimensions, such as the equivalence of closed and proper interval graphs. These formulations enable significant applications, including finding conditions for the sortability of d-independence complexes, constructions of normal Cohen-Macaulay domains linked to d-unit interval graphs, and forbidden subgraph theorems establishing chordality and d-claw-freeness. Our work advances the connections between graph theory, simplicial complexes, and commutative algebra, offering new insights into the algebraic underpinnings of combinatorial structures.
format	Preprint
id	arxiv_https___arxiv_org_abs_2510_16722
institution	arXiv
publishDate	2025
record_format	arxiv
spellingShingle	Generalizations of interval and proper interval graphs for simplicial complexes Ghasr, Fahimeh Khosh-Ahang Combinatorics Commutative Algebra We introduce and investigate generalizations of interval and proper interval graphs to simplicial complexes, including strong interval, unit interval, and under closed variants. Through equivalent combinatorial and algebraic characterizations, we uncover hierarchies among these classes and extend key results to higher dimensions, such as the equivalence of closed and proper interval graphs. These formulations enable significant applications, including finding conditions for the sortability of d-independence complexes, constructions of normal Cohen-Macaulay domains linked to d-unit interval graphs, and forbidden subgraph theorems establishing chordality and d-claw-freeness. Our work advances the connections between graph theory, simplicial complexes, and commutative algebra, offering new insights into the algebraic underpinnings of combinatorial structures.
title	Generalizations of interval and proper interval graphs for simplicial complexes
topic	Combinatorics Commutative Algebra
url	https://arxiv.org/abs/2510.16722

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