Let G = (V, E) be bipartite graph, with vertex partition V = X u Y. Assumefurther thatevery r in X has the same degree dx 2 1, and• every y in Y has the same degree dy > 1.(a) Prove that = .(b) Assuming without loss of generality that dx > dy, show that there exists atleast one matching M C E with number of edges |M|= |X|.

Let GV,E be a bipartite graph, with vertex partition V=X∪Y.And every x in X has the same degree dx≥1…

Let G = (V, E) be bipartite graph, with vertex partition V = XuY. Assume further that • every z in X has the same degree dx 2 1, and • every y in Y has the same degree dy 21. (a) Prove that = %3D (b) Assuming without loss of generality that dx > dy, show that there exists at least one matching M C E with number of edges |M| = |X|.

Let G = (V, E) be bipartite graph, with vertex partition V = XuY. Assume further that • every z in X has the same degree dx 2 1, and • every y in Y has the same degree dy 21. (a) Prove that = %3D (b) Assuming without loss of generality that dx > dy, show that there exists at least one matching M C E with number of edges |M| = |X|.

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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Question

Let G = (V, E) be bipartite graph, with vertex partition V = X u Y. Assume
further that
every r in X has the same degree dx 2 1, and
• every y in Y has the same degree dy > 1.
(a) Prove that = .
(b) Assuming without loss of generality that dx > dy, show that there exists at
least one matching M C E with number of edges |M|= |X|.

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