Finding big matchings in planar graphs quickly
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It is well-known that every n-vertex planar graph with minimum degree 3 has a matching of size at least n/3. But all proofs of this use the Tutte-Berge-formula for the size of a maximum matching. Hence these proofs are not directly algorithmic, and to find such a matching one must apply a general-purposes maximum matching algorithm, which has run-time O(n^1.5α(n)) for planar graphs. In contrast to this, this paper gives a linear-time algorithm that finds a matching of size at least n/3 in any planar graph with minimum degree 3.
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