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# Forests and Eulerian Graphs

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Let F be a forest. Add a vertex x to F and join x to each vertex of odd degree in F. Prove that the graph obtained in this way is randomly Eulerian from x, and every graph randomly Eulerian from x can be obtained in this way.

https://brainmass.com/math/graphs-and-functions/forests-eulerian-graphs-145701

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(1)
Proof that a graph G obtained by adding a vertex V to a forest F and connecting V with each vertex of odd degree in F is Eulerian and V is a randomly Eulerian vertex in it.

A forest is a disjoint union of trees, and a tree is a a graph in which any two vertices are ...

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