Uniquely partitionable graphs

Jozef Bucko ; Marietjie Frick ; Peter Mihók ; Roman Vasky

Discussiones Mathematicae Graph Theory, Tome 17 (1997), p. 103-113 / Harvested from The Polish Digital Mathematics Library

Résumé

Let ₁,...,ₙ be properties of graphs. A (₁,...,ₙ)-partition of a graph G is a partition of the vertex set V(G) into subsets V₁, ...,Vₙ such that the subgraph $G[V_i]$ induced by $V_i$ has property $_i$; i = 1,...,n. A graph G is said to be uniquely (₁, ...,ₙ)-partitionable if G has exactly one (₁,...,ₙ)-partition. A property is called hereditary if every subgraph of every graph with property also has property . If every graph that is a disjoint union of two graphs that have property also has property , then we say that is additive. A property is called degenerate if there exists a bipartite graph that does not have property . In this paper, we prove that if ₁,..., ₙ are degenerate, additive, hereditary properties of graphs, then there exists a uniquely (₁,...,ₙ)-partitionable graph.

Détail

Publié le : 1997-01-01

Zbl 0906.05057

EUDML-ID : urn:eudml:doc:270374

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