Maximal graphs with respect to hereditary properties
Izak Broere ; Marietjie Frick ; Gabriel Semanišin
Discussiones Mathematicae Graph Theory, Tome 17 (1997), p. 51-66 / Harvested from The Polish Digital Mathematics Library
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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 Vi has property Pi; 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.

Publié le : 1997-01-01
EUDML-ID : urn:eudml:doc:270401 
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Izak Broere; Marietjie Frick; Gabriel Semanišin. Maximal graphs with respect to hereditary properties. Discussiones Mathematicae Graph Theory, Tome 17 (1997) pp. 51-66. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1038/

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