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3.1.10. Let M and N be matchings in a graph G, with |M| > |N|. Prove that there exist matchings M' and N' in G such that |M'| = |M| – 1, |N'| = |N|+ 1, and M', N' have the same union and intersection (as edge sets) as M, N. %3D

3.1.10. Let M and N be matchings in a graph G, with |M| > |N|. Prove that there exist matchings M' and N' in G such that |M'| = |M| – 1, |N'| = |N|+ 1, and M', N' have the same union and intersection (as edge sets) as M, N. %3D

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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3.1.10. Let M and N be matchings in a graph G, with |M| > |N|. Prove that there exist matchings M' and N' in G such that |M'| = |M| – 1, |N'| = |N|+ 1, and M', N' have the same union and intersection (as edge sets) as M, N.
Transcribed Image Text:3.1.10. Let M and N be matchings in a graph G, with |M| > |N|. Prove that there exist matchings M' and N' in G such that |M'| = |M| – 1, |N'| = |N|+ 1, and M', N' have the same union and intersection (as edge sets) as M, N.
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