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On hereditary properties of composition graphs

Vadim E. LevitEugen Mandrescu — 1998

Discussiones Mathematicae Graph Theory

The composition graph of a family of n+1 disjoint graphs H i : 0 i n is the graph H obtained by substituting the n vertices of H₀ respectively by the graphs H₁,H₂,...,Hₙ. If H has some hereditary property P, then necessarily all its factors enjoy the same property. For some sort of graphs it is sufficient that all factors H i : 0 i n have a certain common P to endow H with this P. For instance, it is known that the composition graph of a family of perfect graphs is also a perfect graph (B. Bollobas, 1978), and the...

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