Projection properties of graphs without either triangle or square
type: Item
instance of: scholarly article
title: Projection properties of graphs without either triangle or square
zbMATH Open document ID: 0851.05091
author: Christian Delhommé
published in: European Journal of Combinatorics
publication date: 1996-03-18T00:00:00Z
review text: The notion of projection property, which was introduced in 1990 by \textit{E. Corominas} [C. R. Acad. Sci. Paris 311, Sér. I, 199-204 (1990)] for ordered sets, is considered by this author in the context of graphs without either triangle or square. The main result proven is stated as follows: Let \(G\) be a graph without either triangle or square. The following conditions are equivalent: (i) \(G\) verifies \(\text{PPC}_2\). (ii) \(G\) verifies \(\text{PPA}_2\). (iii) \(G\) verifies \(\text{PPA}_n\) for all \(n\). (iv) \(G\) is connected and, for every edge whose omission disconnects it, not one of the two corresponding connected components is a tree. The reader is referred to section 2 of the paper for the meaning of \(\text{PPC}_n\) (\(n\)-property of cartesian projection) and \(\text{PPA}_n\) (\(n\)-property of affine projection).
reviewed by: M.Oravas
Mathematics Subject Classification ID: 05C99
zbMATH DE Number: 847627
zbMATH Keywords: projection property
zbMATH Keywords: cartesian projection
zbMATH Keywords: affine projection
MaRDI profile type: Publication
full work available at URL: eujc.1996.0002
OpenAlex ID: W2058631460
DOI: 10.1006/EUJC.1996.0002
description: scientific article; zbMATH DE number 847627