An Upper Bound for the Excessive Index of an r-Graph
We construct a family of r-graphs having a minimum 1-factor cover of cardinality (disproving a conjecture of Bonisoli and Cariolaro, Birkhuser, Basel, 2007, 7384). Furthermore, we show the equivalence between the statement that is the best possible upper bound for the cardinality of a minimum 1-factor cover of an r-graph and the well-known generalized BergeFulkerson conjecture.
excessive index r-graphs generalized bergefulkerson conjecture perfect matchings