TESU Graphs Set of Proofs for problems questions

Question Description

I’m working on a graphs multi-part question and need an explanation and answer to help me learn.

Instructions

Write a complete set of proofs for problems

Q1: Let G be a simple graph on 2k vertices containing no triangles. Prove, by induction on k, that G has at most k2 edges, and give an example of a graph for which this upper bound is achieved. (This result is often called Turs extremal theorem.)

Q2: Prove that, if two distinct cycles of a graph G each contain an edge e, then G has a cycle that does not contain e.

For each proof complete the following:

– State the hypotheses

– State the conclusions

– Clearly and precisely prove the conclusions from the hypotheses

– Results presented earlier in the text may be used and must be clearly documented

Explanation & Answer:

2 Questions

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