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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...
We introduce a new hereditary class of graphs, the dominant-matching graphs, and we characterize it in terms of forbidden induced subgraphs.
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