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Combinatorics of Local Search: An Optimal 4-Local Hall's Theorem for Planar Graphs
2017
European Symposium on Algorithms
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Local search for combinatorial optimization problems is becoming a dominant algorithmic paradigm, with several papers using it to resolve long-standing open problems. In this paper, we prove the following '4-local' version of Hall's theorem for planar graphs: given a bipartite planar graph G = (B, R, E) such that |N (B )| ≥ |B | for all |B | ≤ 4, there exists a matching of size at least |B| 4 in G; furthermore this bound is tight. Besides immediately implying improved bounds for several
doi:10.4230/lipics.esa.2017.8
dblp:conf/esa/AntunesMM17
fatcat:e2qih4zavnft3lb4j2lzyzwdza