Combinatorics of Local Search: An Optimal 4-Local Hall's Theorem for Planar Graphs
نویسندگان
چکیده
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 problems studied in previous papers, we find this variant of Hall’s theorem to be of independent interest in graph theory. 1998 ACM Subject Classification F.2.2 Nonnumerical Algorithms and Problems
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