Let M be a subset of X (where XUY is the vertex set of a bipartite graph) Let all of M be matched by a matching in the graph. If IM1] < |M2| (where M1 and M2 are independent sets). Consider matchings in the subgraph of the bipartite graph induced on the vertices of M1 U M2 and show, using maximum cardinality, that there exists x E M2\M1 such that M1 U (x} is independent.
Let M be a subset of X (where XUY is the vertex set of a bipartite graph) Let all of M be matched by a matching in the graph. If IM1] < |M2| (where M1 and M2 are independent sets). Consider matchings in the subgraph of the bipartite graph induced on the vertices of M1 U M2 and show, using maximum cardinality, that there exists x E M2\M1 such that M1 U (x} is independent.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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