On complexity of special maximum matchings constructing
R.R. Kamalian, V. V. Mkrtchyan
TL;DR
This paper investigates the computational complexity of determining whether a maximum matching in bipartite graphs can be removed to achieve a specified bound on the remaining maximum matching size, establishing NP-completeness.
Contribution
It proves that the problem of finding such maximum matchings with bounds is NP-complete for bipartite graphs, highlighting its computational difficulty.
Findings
NP-completeness for bipartite graphs
Difficulty in constructing maximum matchings with bounds
Theoretical complexity result
Abstract
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.
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