Let m be a positive integer and let G be a graph. A set M of matchings of G, all of which of size m, is called an [m]-covering of G if ⋃ M∈MM = E(G). G is called [m]-coverable if it has an [m]-covering. An [m]-covering M such that |M| is minimum is called an excessive [m]-factorization of G and the number of matchings it contains is a graph parameter called excessive [m]-index and denoted by χ[...

‎The excessive index of a bridgeless cubic graph $G$ is the least integer $k$‎, ‎such that $G$ can be covered by $k$ perfect matchings‎. ‎An equivalent form of Fulkerson conjecture (due to Berge) is that every bridgeless‎ ‎cubic graph has excessive index at most five‎. ‎Clearly‎, ‎Petersen graph is a cyclically 4-edge-connected snark with excessive index at least 5‎, ‎so Fouquet and Vanherpe as...

Background: Saffron is widely used as a food flavor and has well known medicinal effects which have an effect on steroid and sexual hormones. The aim of present study was investigation of saffron orally administration on spermatogenesis index in stress induced rats. Materials and Methods: In present study, 160 male adult rats divided to four groups with 10 rats per each cage and with four repli...

Let m be a positive integer and let G be a cubic graph of order 2n. We consider the problem of covering the edge-set of G with the minimum number of matchings of size m. This number is called the excessive [m]-index of G in the literature. The case m = n, that is, a covering with perfect matchings, is known to be strictly related to an outstanding conjecture of Berge and Fulkerson. In this pape...