Note on Counting Eulerian Circuits
Graham R. Brightwell, Peter Winkler
TL;DR
This paper establishes that counting Eulerian circuits in undirected graphs is a computationally complex problem classified as #P-complete, highlighting its difficulty in computational complexity theory.
Contribution
It proves the #P-completeness of counting Eulerian circuits, a significant complexity classification result for this problem.
Findings
Counting Eulerian circuits is #P-complete.
The problem is computationally intractable in general.
This classification impacts algorithms for related graph problems.
Abstract
We show that the problem of counting the number of Eulerian circuits in an undirected graph is complete for the class #P.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMarkov Chains and Monte Carlo Methods · Advanced Graph Theory Research · Limits and Structures in Graph Theory