A simple way to tell a simple polytope from its graph
type: Item
instance of: scholarly article
title: A simple way to tell a simple polytope from its graph
zbMATH Open document ID: 0673.05087
DOI: 10.1016/0097-3165(88)90064-7
author: Gil Kalai
published in: Journal of Combinatorial Theory. Series A
publication date: 1988-01-01T00:00:00Z
review text: Let P be a simple d-dimensional polytope and G(P) be the graph of P. Two vertices u and v in V(P) are adjacent in G(P) if [v,u] is a 1-dimensional face of P. Recently, \textit{R. Blind} and \textit{P. Mani-Levitska} [Aequationes Math. 34, 287-297 (1987; Zbl 0634.52005)] proved a conjecture of Perles that G(P) determines the entire combinatorial structure of P. In this note the author gives a simple proof of this result.
Mathematics Subject Classification ID: 05C99
zbMATH DE Number: 4101271
zbMATH Keywords: acyclic orientation
zbMATH Keywords: regular graph
zbMATH Keywords: polytope
Wikidata QID: Q60358418
reviewed by: Louis Caccetta
MaRDI profile type: Publication
full work available at URL: 0097-3165(88)90064-7
OpenAlex ID: W2074536752
cites work: Puzzles and polytope isomorphisms
cites work: Q4747150
cites work: Triangulated n-manifolds are determined by their \([n/2]+1\)-skeletons
cites work: Q5547252
DBLP publication ID: journals/jct/Kalai88a
description: scientific article; zbMATH DE number 4101271