\r\nmatching M whose matched vertices induces a sub-graph which has

\r\nonly one perfect matching. In this paper, we make progress on the

\r\nopen question of the status of this problem on interval graphs (graphs

\r\nobtained as the intersection graph of intervals on a line). We give

\r\nan algorithm to compute maximum cardinality uniquely restricted

\r\nmatchings on certain sub-classes of interval graphs. We consider two

\r\nsub-classes of interval graphs, the former contained in the latter, and

\r\ngive O(|E|^2) time algorithms for both of them. It is to be noted that

\r\nboth sub-classes are incomparable to proper interval graphs (graphs

\r\nobtained as the intersection graph of intervals in which no interval

\r\ncompletely contains another interval), on which the problem can be

\r\nsolved in polynomial time.","references":null,"publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 114, 2016"}