5
$\begingroup$

I have an undirected graph with $n$ vertices and $m$ edges. How to determinate in $poly (n, m)$, is it possible (and how is it necessary) to orient all the edges so that each vertex has the same outgoing and incoming degree.

$\endgroup$
7
$\begingroup$

If such an orientation is possible, then all degrees are even. Conversely, if all degrees are even then the graph is Eulerian. Orient the edges according to an Eulerian circuit.

$\endgroup$
0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.