Graphs and Vector Calculus
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Please help answer the following question. Provide step by step calculations along with detailed explanations to explain how each step works.
If all edges of Kn (a complete graph) have been coloured red and blue, how do we show that either the red graph or the blue graph is connected?
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Solution Summary
This posting helps with a vector calculus problem that involving showing whether one of multiple graphs are connected. This is done through a method called induction. Step by step calculations with detailed explanations are given. The solution is written up using the program, Latex.
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Problem: If all edges of Kn (a complete graph) have been coloured red and blue, how do we show that either the red graph or the blue graph is connected?
Solution:
I thought induction was the best way to do this one.
I used LaTeX to generate a PDF file. Please see attachment.
Proposition. If Kn, the complete graph on n vertices, is colored in such away that every edge is either red or blue, then either the red component or the blue ...
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