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There is a vertex v in a bipartite graph G=(V,E) with deg(v)=m+n, where m = |V2I. |V₁|,n=

There is a vertex v in a bipartite graph G=(V,E) with deg(v)=m+n, where m = |V2I. |V₁|,n=

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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2. Decide if the statement is True or False. Justify your answer. Explain why is it true or why not, and give an example/counterexample where necessary. a) Does the poset (P(Z), ≤) have mimmal element(s)? There is a vertex v in a bipartite graph G=(V,E) with deg(v)=m+n, where m = |V₂l. c) The sum of all vertex degrees in an undirected graph is always even number. d) Kn has a Hamiltonian circuit for every natural number n ≥ 3. |V₁|, n = =
Transcribed Image Text:2. Decide if the statement is True or False. Justify your answer. Explain why is it true or why not, and give an example/counterexample where necessary. a) Does the poset (P(Z), ≤) have mimmal element(s)? There is a vertex v in a bipartite graph G=(V,E) with deg(v)=m+n, where m = |V₂l. c) The sum of all vertex degrees in an undirected graph is always even number. d) Kn has a Hamiltonian circuit for every natural number n ≥ 3. |V₁|, n = =
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Can you explain the solution a bit more as I am not understanding how you proved it to be false?

 

Is it false cause degree m+n would imply a vertex in M or N that has edges contained within the subset which breaks definition of bipartite?

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