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Now consider the following bipartite graph. 26 25 24 23 Առ ขา 06 Us 04 03 V2 U1 (b) Show that M = {u₁v1, u2v2, u4V4, u5u5} is a matching of this graph. {U1V1, (c) Find a perfect matching of the graph, or explain why such a matching does not exist. Show your working. Recall that a graph G is called k-regular, for ke N, if dc (v) = k for all vЄ V(G). (d) Using Hall's theorem or otherwise, prove that every k-regular bipartite graph has a perfect matching.

Now consider the following bipartite graph. 26 25 24 23 Առ ขา 06 Us 04 03 V2 U1 (b) Show that M = {u₁v1, u2v2, u4V4, u5u5} is a matching of this graph. {U1V1, (c) Find a perfect matching of the graph, or explain why such a matching does not exist. Show your working. Recall that a graph G is called k-regular, for ke N, if dc (v) = k for all vЄ V(G). (d) Using Hall's theorem or otherwise, prove that every k-regular bipartite graph has a perfect matching.

Advanced Engineering Mathematics
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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Now consider the following bipartite graph. 26 25 24 23 Առ ขา 06 Us 04 03 V2 U1 (b) Show that M = {u₁v1, u2v2, u4V4, u5u5} is a matching of this graph. {U1V1, (c) Find a perfect matching of the graph, or explain why such a matching does not exist. Show your working. Recall that a graph G is called k-regular, for ke N, if dc (v) = k for all vЄ V(G). (d) Using Hall's theorem or otherwise, prove that every k-regular bipartite graph has a perfect matching.
Transcribed Image Text:Now consider the following bipartite graph. 26 25 24 23 Առ ขา 06 Us 04 03 V2 U1 (b) Show that M = {u₁v1, u2v2, u4V4, u5u5} is a matching of this graph. {U1V1, (c) Find a perfect matching of the graph, or explain why such a matching does not exist. Show your working. Recall that a graph G is called k-regular, for ke N, if dc (v) = k for all vЄ V(G). (d) Using Hall's theorem or otherwise, prove that every k-regular bipartite graph has a perfect matching.
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