Proof: By Induction

(related to Proposition: Equivalent Definitions of Trees)

By hypothesis, $G(V,E,\gamma)$ is an undirected graph.

$(1)\Rightarrow(2)$

$(2)\Rightarrow(3)$

$(3)\Rightarrow(4)$

$(4)\Rightarrow(5)$

$(5)\Rightarrow(6)$

$(6)\Rightarrow(1)$


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References

Bibliography

  1. Krumke S. O., Noltemeier H.: "Graphentheoretische Konzepte und Algorithmen", Teubner, 2005, 1st Edition