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3 votes

How to find a random cycle in a large graph?

This answer is about directed simple cycles, meaning that the only repeated vertices are the first and last ones. First, there's no general efficient algorithm to sample uniformly a directed simple cy …
Elle Najt's user avatar
  • 1,462
6 votes
3 answers
2k views

Number of self avoiding paths on a grid graph?

Let $G$ be an $n \times n$ grid graph. Is there anything known about the asymptotic growth rate of the number of self avoiding paths from $(0,0)$ to $(n,b)$ (from the lower left corner to some arbitra …
Elle Najt's user avatar
  • 1,462