  Finding maximum-cardinality matchings in undirected graphs is arguably one of
the most central graph problems. For general m-edge and n-vertex graphs, it is
well-known to be solvable in $O(m \sqrt{n})$ time. We develop a linear-time
algorithm to find maximum-cardinality matchings on cocomparability graphs, a
prominent subclass of perfect graphs that contains interval graphs as well as
permutation graphs. Our algorithm is based on the recently discovered
Lexicographic Depth First Search (LDFS).
