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

A Linear-Time Algorithm for Maximum-Cardinality Matching on Cocomparability Graphs