Unformatted text preview: CS 473: Algorithms, Fall 2010 HBS 10 Problem 1 . [kRegular Bipartite Graphs] A kRegular graph is an undirected graph where every vertex has degree k . We will prove that if a bipartite graph is kRegular, then it has a perfect matching. First, recall the following definitions: Bipartite Graph : a graph whose vertices are partitioned into two independent sets, L and R . Matching : A matching in a graph G is a set of edges such that no two edges share a common vertex. Neighbors : Let v be a vertex. The neighbors of v , denoted by N ( v ) are the set of vertices connected to v . Hall’s Theorem : Let G = ( L ∪ R,E ) be a bipartite graph where  L  =  R  . Then G has a perfect matching if and only if for every subset X ⊆ L ,  N ( X )  ≥  X  . For the following problems, let G = ( L ∪ R,E ) be a kregular bipartite graph where  L  =  R  . 1. Show that the G has a perfect matching via Hall’s theorem....
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 Fall '08
 Chekuri,C
 Algorithms, two days, pj, Bipartite graph, perfect matching

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