hbs10 - CS 473: Algorithms, Fall 2010 HBS 10 Problem 1 ....

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: CS 473: Algorithms, Fall 2010 HBS 10 Problem 1 . [k-Regular Bipartite Graphs] A k-Regular graph is an undirected graph where every vertex has degree k . We will prove that if a bipartite graph is k-Regular, 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 . Halls 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 k-regular bipartite graph where | L | = | R | . 1. Show that the G has a perfect matching via Halls theorem....
View Full Document

This note was uploaded on 01/22/2011 for the course CS 473 taught by Professor Chekuri,c during the Fall '08 term at University of Illinois, Urbana Champaign.

Ask a homework question - tutors are online