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3. (a) Prove that for k > 2, for every tree T with k vertices, every graph G with minimum degree at least k - 1 contains a subgraph isomorphic to T. (b) Show that "k-1" in part (a) is best possible (for every k > 2).

3. (a) Prove that for k > 2, for every tree T with k vertices, every graph G with minimum degree at least k - 1 contains a subgraph isomorphic to T. (b) Show that "k-1" in part (a) is best possible (for every k > 2).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Need help with part (b). Please explain each step and neatly type up. Thank you :)

 

3. (a) Prove that for k > 2, for every tree T with k vertices, every graph G with minimum degree at least k - 1 contains a subgraph isomorphic to T.
Transcribed Image Text:3. (a) Prove that for k > 2, for every tree T with k vertices, every graph G with minimum degree at least k - 1 contains a subgraph isomorphic to T.
(b) Show that "k-1" in part (a) is best possible (for every k > 2).
Transcribed Image Text:(b) Show that "k-1" in part (a) is best possible (for every k > 2).
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