{"id":"palomar/PALOMAR-2026-10-27-000026","url":"https://github.com/benjamin-dozier/birthday-nonbacktracking/tree/7f4be1aae157cadcbb9511bd6b9ee187d60fb662","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-27-000026-v1.json","repo":"https://github.com/benjamin-dozier/birthday-nonbacktracking","tags":["math.CO"],"score":0,"title":"birthday-paradox-non-backtracking-regular-graphs","trust":"high","domain":"math.CO","source":"palomar","authors":["Benjamin Dozier"],"reviews":0,"subject":"math.CO","summary":"A Lean 4 and Mathlib formalization (found by Codex GPT 5.6 Sol) of the main theorem of the author's recent arxiv preprint arXiv:2608.26321. This is the Birthday Paradox for non-backtracking walks on regular graphs of degree at least 3: such a walk of length k has high probability of self-intersecting when k is significantly greater than sqrt(n), where n is the number of vertices of the graph. This resolves a conjecture of Noga Alon and Yuval Peres for the fixed degree case.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-27","reactions":{},"formalized":true,"formalizes":[{"title":"The Birthday Paradox for non-backtracking walks on regular graphs","identifier":"arXiv:2608.26321","relationship":"formalizes"}]}