On uniquely partitionable planar graphs
type: Item
instance of: scholarly article
title: On uniquely partitionable planar graphs
zbMATH Open document ID: 0957.05029
DOI: 10.1016/S0012-365X(98)00102-2
author: Peter Mihók
author: Jozef Bucko
author: Margit Voigt
published in: Discrete Mathematics
publication date: 2000-11-02T00:00:00Z
review text: Let \({\mathcal P}_1,{\mathcal P}_2,\dots,{\mathcal P}_n\); \(n\geq 2\) be any properties of graphs. A vertex \(({\mathcal P}_1,{\mathcal P}_2,\dots,{\mathcal P}_n)\)-partition of a graph \(G\) is a partition \((V_1,V_2,\dots, V_n)\) of \(V(G)\) such that for each \(i= 1,2,\dots, n\) the induced subgraph \(G[V_i]\) has the property \({\mathcal P}_i\). A graph \(G\) is said to be uniquely \(({\mathcal P}_1,{\mathcal P}_2,\dots,{\mathcal P}_n)\)-partitionable if \(G\) has unique vertex \(({\mathcal P}_1,{\mathcal P}_2,\dots,{\mathcal P}_n)\)-partition. In the present paper we investigate the problem of the existence of uniquely \(({\mathcal P}_1,{\mathcal P}_2,\dots,{\mathcal P}_n)\)-partitionable planar graphs for additive and hereditary properties \({\mathcal P}_1,{\mathcal P}_2,\dots,{\mathcal P}_n\) of graphs. Some constructions and open problems are presented for \(n= 2\).
Mathematics Subject Classification ID: 05C10
Mathematics Subject Classification ID: 05C15
zbMATH DE Number: 1524994
zbMATH Keywords: uniquely partitionable planar graphs
zbMATH Keywords: partition
zbMATH Keywords: hereditary properties
MaRDI profile type: Publication
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full work available at URL: s0012-365x(98)00102-2
OpenAlex ID: W2081899314
description: scientific article; zbMATH DE number 1524994