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On a perfect problem

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Zverovich I.

Discussiones Mathematicae Graph Theory

2006

tom 26

nr 2

273-277

We solve Open Problem (xvi) from Perfect Problems of Chvátal [1] available at ftp://dimacs.rutgers.edu/pub/perfect/problems.tex: Is there a class C of perfect graphs such that (a) C does not include all perfect graphs and (b) every perfect graph contains a vertex whose neighbors induce a subgraph that belongs to C? A class P is called locally reducible if there exists a proper subclass C of P such that every graph in P contains a local subgraph belonging to C. We characterize locally reducible hereditary classes. It implies that there are infinitely many solutions to Open Problem (xvi). However, it is impossible to find a hereditary class C of perfect graphs satisfying both (a) and (b).

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1 Discussiones Mathematicae Graph Theory

1 Zverovich I.

1 2006

Wyniki wyszukiwania

On a perfect problem