Combinatorics of Local Search: An Optimal 4-Local Hall's Theorem for Planar Graphs

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… CONTINUE READING