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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 math formula (disproving a conjecture of Bonisoli and Cariolaro, Birkhäuser, Basel, 2007, 73–84). Furthermore, we show the equivalence between the statement that math formula 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.