Discussiones Mathematicae Graph Theory 26(2) (2006)
ON A PERFECT PROBLEM
Igor E. Zverovich
RUTCOR - Rutgers Center for Operations Research, Rutgers
The State University of New Jersey
640 Bartholomew Road, Piscataway, NJ 08854-8003, USA
AbstractWe solve Open Problem (xvi) from Perfect Problems of Chvátal  available at ftp://dimacs.rutgers.edu/pub/perfect/problems.tex:
Is there a class C of perfect graphs such that
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).
Keywords: hereditary classes, perfect graphs.
2000 Mathematics Subject Classification: 05C17 (Perfect graphs).
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Received 6 September 2005
Revised 15 March 2006