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.
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