Tell me more ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.
up vote 0 down vote favorite

Does the graph with only one vertex has an Eulerian path?
And i think he has an Hamiltonian path, right?
Cheers.

share|improve this question
1  
I don't know if everyone defines it the same way, but Diestel's book, at least, allows a path to consist of a single vertex, which means that the answer is yes. – Andrew Uzzell Dec 12 '12 at 14:48
@Andrew: You could post that as an answer so the question doesn't remain unanswered. – joriki Dec 12 '12 at 17:34

1 Answer

up vote 1 down vote accepted

I'm not sure if all graph theory books treat degenerate cases the same way, but Diestel's Graph Theory, at least, allows a path to have length $0$, i.e., to consist of a single vertex with no edges. If a graph consists of a single vertex $v$, then the a path consisting of $v$ is vacuously Eulerian. It is also a Hamiltonian path, since it contains all of the vertices of the graph.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

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