An inequality related to the pairs of matchings of a graph - Rafael R. Kamalian; Vahan V. Mkrtchyan (Изд-во НАН РА)
For a given graph disjoint pairs of matchings the union of which contains as many edges as possible are considered. It is shown that the relation of the cardinality of a maximum matching to the cardinality of the largest matching in those pairs does not exceed 3=2. A conjecture is posed which states that this coe±cient can be replaced by 5=4 . Finally, a family of graphs is presented which shows that the abovementioned coe±cient can not be replaced by a constant which is smaller than 5=4.
Keywords: Mathematics; Graph theory