Swapnil Gupta and C. Pandu Rangan
Computing Maximum Uniquely Restricted Matchings in Restricted Interval Graphs
980 - 989
2016
10
6
International Journal of Computer and Information Engineering
https://publications.waset.org/pdf/10004512
https://publications.waset.org/vol/114
World Academy of Science, Engineering and Technology
A uniquely restricted matching is defined to be a
matching M whose matched vertices induces a subgraph which has
only one perfect matching. In this paper, we make progress on the
open question of the status of this problem on interval graphs (graphs
obtained as the intersection graph of intervals on a line). We give
an algorithm to compute maximum cardinality uniquely restricted
matchings on certain subclasses of interval graphs. We consider two
subclasses of interval graphs, the former contained in the latter, and
give O(E2) time algorithms for both of them. It is to be noted that
both subclasses are incomparable to proper interval graphs (graphs
obtained as the intersection graph of intervals in which no interval
completely contains another interval), on which the problem can be
solved in polynomial time.
Open Science Index 114, 2016