We construct a family of r-graphs having a minimum 1-factor cover of cardinality 2r − 1 (disproving a conjecture of Bonisoli and Cariolaro,Birkhauser, Basel, 2007, 73–84). Furthermore, we show the equivalence between the statement that 2r − 1 is the best possible upper bound for the cardinality of a minimum 1-factor cover of an r-graph and the well-known generalized Berge–Fulkerson conjecture.

An upper bound for the excessive index of an r-graph

Mazzuoccolo, Giuseppe
2013-01-01

Abstract

We construct a family of r-graphs having a minimum 1-factor cover of cardinality 2r − 1 (disproving a conjecture of Bonisoli and Cariolaro,Birkhauser, Basel, 2007, 73–84). Furthermore, we show the equivalence between the statement that 2r − 1 is the best possible upper bound for the cardinality of a minimum 1-factor cover of an r-graph and the well-known generalized Berge–Fulkerson conjecture.
perfect matchings, r-graph, Berge-Fulkerson conjecture
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/927866
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