# Rhemz Report - d b Columns b2Columns b3y1 y1 e c b4y2 y2 f...

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d e f A B C D E Graduates Jobs b c d e f A B C D E Columns y1 y2 y3 y4 y5 x1 x2 x3 x4 b2 b3 b4 b5 b6 w7 w3 w4 w5 w6 w1 w2 Columns y1 y2 y3 y4 y5 x1 x2 x3 x4 Remalyn Quinay-Casem Graph Theory and Combinatorics MATCHINGS IN BIPARTITE GRAPHS Definition of a Bipartite Graph bipartite graph  is prescribed by i. a set of vertices ii. a partition of that set of vertices into two parts; and iii. a set of edges joining a vertex in one part to a vertex in the other part. Problem 1:   Just say there are five computer science graduates A, B, C, D and E, and six advertised  positions  a b c d e  and  f . Assume that:  A is qualified for jobs  a  and  d B is qualified for jobs  a  and  c C is qualified for jobs  b  and  f D is qualified for jobs  b d  and  e E is qualified for jobs  c  and  f . Is it possible that everyone will get a job for which they are qualified?  To study such a  matching problem , begin by constructing a bipartite graph, as follows. Definition of Matching Let  G  be a bipartite graph, a  matching  of  G  is a set of edges no two of which share an end. 1 | P a g e

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Remalyn Quinay-Casem Graph Theory and Combinatorics The good news:  Every CS graduate gets a job! Problem 2:
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## This note was uploaded on 03/11/2010 for the course MATH Math 102 taught by Professor Dr.raquel during the Spring '10 term at University of the Philippines Diliman.

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Rhemz Report - d b Columns b2Columns b3y1 y1 e c b4y2 y2 f...

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