Maximal graphs with respect to hereditary properties

• Autorzy: Izak Broere , Marietjie Frick , Gabriel Semanišin
• Języki publikacji: EN

Abstrakty

EN

A property of graphs is a non-empty set of graphs. A property P is called hereditary if every subgraph of any graph with property P also has property P. Let P₁, ...,Pₙ be properties of graphs. We say that a graph G has property P₁∘...∘Pₙ if the vertex set of G can be partitioned into n sets V₁, ...,Vₙ such that the subgraph of G induced by V_i has property $P_i$; i = 1,..., n. A hereditary property R is said to be reducible if there exist two hereditary properties P₁ and P₂ such that R = P₁∘P₂. If P is a hereditary property, then a graph G is called P- maximal if G has property P but G+e does not have property P for every e ∈ E([G̅]). We present some general results on maximal graphs and also investigate P-maximal graphs for various specific choices of P, including reducible hereditary properties.

Słowa kluczowe

EN

hereditary property of graphs   maximal graphs   vertex partition  

Kategorie tematyczne

• 05C15: Coloring of graphs and hypergraphs

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 1997
• Tom: 17
• Numer: 1
• Strony: 51-66

Daty

wydano

1997

otrzymano

1997-03-13

Twórcy

autor

Izak Broere

• Department of Mathematics, Rand Afrikaans University, P.O. Box 524, Auckland Park, 2006 South Africa

autor

Marietjie Frick

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

autor

Gabriel Semanišin

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

Bibliografia

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Identyfikatory

DOI

10.7151/dmgt.1038