Uniquely partitionable graphs

• Autorzy: Jozef Bucko , Marietjie Frick , Peter Mihók , Roman Vasky
• Języki publikacji: EN

Abstrakty

EN

Let 𝓟₁,...,𝓟ₙ be properties of graphs. A (𝓟₁,...,𝓟ₙ)-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 $𝓟_i$; i = 1,...,n. A graph G is said to be uniquely (𝓟₁, ...,𝓟ₙ)-partitionable if G has exactly one (𝓟₁,...,𝓟ₙ)-partition. A property 𝓟 is called hereditary if every subgraph of every graph with property 𝓟 also has property 𝓟. If every graph that is a disjoint union of two graphs that have property 𝓟 also has property 𝓟, then we say that 𝓟 is additive. A property 𝓟 is called degenerate if there exists a bipartite graph that does not have property 𝓟. In this paper, we prove that if 𝓟₁,..., 𝓟ₙ are degenerate, additive, hereditary properties of graphs, then there exists a uniquely (𝓟₁,...,𝓟ₙ)-partitionable graph.

Słowa kluczowe

EN

hereditary property of graphs; additivity; reducibility; vertex partition

Kategorie tematyczne

• 05C15: Coloring of graphs and hypergraphs
• 05C70: Factorization, matching, partitioning, covering and packing

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 1997
• Tom: 17
• Numer: 1
• Strony: 103-113

Daty

wydano

1997

otrzymano

1997-01-03

poprawiono

1997-04-25

Twórcy

autor

Jozef Bucko

• Department of Geometry and Algebra, P.J. Šafárik University, Jesenná 5, 041 54 Košice, Slovak Republic

autor

Marietjie Frick

• Department of Mathematics, Applied Mathematics and Astronomy, University of South Africa, P.O. Box 392, Pretoria, 0001 South Africa

autor

Peter Mihók

• Department of Geometry and Algebra, P.J. Šafárik University, Jesenná 5, 041 54 Košice, Slovak Republic

autor

Roman Vasky

• Department of Geometry and Algebra, P.J. Šafárik University, Jesenná 5, 041 54 Košice, Slovak Republic

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Identyfikatory

DOI

10.7151/dmgt.1043