On some variations of extremal graph problems

• Autorzy: Gabriel Semanišin
• Języki publikacji: EN

Abstrakty

EN

A set P of graphs is termed hereditary property if and only if it contains all subgraphs of any graph G belonging to P. A graph is said to be maximal with respect to a hereditary property P (shortly P-maximal) whenever it belongs to P and none of its proper supergraphs of the same order has the property P. A graph is P-extremal if it has a the maximum number of edges among all P-maximal graphs of given order. The number of its edges is denoted by ex(n, P). If the number of edges of a P-maximal graph is minimum, then the graph is called P-saturated and its number of edges is denoted by sat(n, P).
In this paper, we consider two famous problems of extremal graph theory. We shall translate them into the language of P-maximal graphs and utilize the properties of the lattice of all hereditary properties in order to establish some general bounds and particular results. Particularly, we shall investigate the behaviour of sat(n,P) and ex(n,P) in some interesting intervals of the mentioned lattice.

Słowa kluczowe

EN

hereditary properties of graphs; maximal graphs; extremal graphs; saturated graphs

Kategorie tematyczne

• 05C15: Coloring of graphs and hypergraphs
• 05C35: Extremal problems

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 1997
• Tom: 17
• Numer: 1
• Strony: 67-76

Daty

wydano

1997

otrzymano

1997-01-03

Twórcy

autor

Gabriel Semanišin

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

Bibliografia

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Identyfikatory

DOI

10.7151/dmgt.1039