4 research outputs found
On complexity of special maximum matchings constructing
For bipartite graphs the NP-completeness is proved for the problem of
existence of maximum matching which removal leads to a graph with given
lower(upper)bound for the cardinality of its maximum matching.Comment: 12 pages, 8 figures. Discrete Mathematics, to appea
On upper bounds for parameters related to construction of special maximum matchings
For a graph let and denote the size of the largest and
smallest maximum matching of a graph obtained from by removing a maximum
matching of . We show that and
provided that contains a perfect matching. We also characterize the class
of graphs for which . Our characterization implies the existence of
a polynomial algorithm for testing the property . Finally we show
that it is -complete to test whether a graph containing a perfect
matching satisfies .Comment: 11 pages, no figure
Supermodularity in Unweighted Graph Optimization I: Branchings and Matchings
The main result of this paper is motivated by the following two apparently unrelated graph optimization problems: (A) As an extension of Edmonds' disjoint branchings theorem, characterize digraphs comprising k disjoint branchings B-i each having a specified number mu(i) of arcs. (B) As an extension of Ryser's maximum term rank formula, determine the largest possible matching number of simple bipartite graphs complying with degree-constraints. The solutions to these problems and to their generalizations will be obtained from a new min-max theorem on covering a supermodular function by a simple degree-constrained bipartite graph. A specific feature of the result is that its minimum cost extension is already NP-hard. Therefore classic polyhedral tools themselves definitely cannot be sufficient for solving the problem, even though they make some good service in our approach