{"id":"palomar/PALOMAR-2026-09-20-000009","url":"https://github.com/jfairfaxball-348/Fischer-Zero-Forcing-Counterexample/tree/4ee012d6941e221d294f26520aff92043d715140","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-09-20-000009-v1.json","repo":"https://github.com/jfairfaxball-348/Fischer-Zero-Forcing-Counterexample","tags":["math.CO","msc:05C50","msc:05C69","combinatorics","graph-theory","zero-forcing","lean"],"score":0,"title":"Fischer's 24-vertex zero-forcing counterexample","trust":"high","domain":"math.CO","source":"palomar","authors":["John Fairfax-Ball"],"reviews":0,"subject":"math.CO","summary":"A Lean 4 formalization of Mikko Fischer's explicit connected 24-vertex subcubic graph with independence number 9 and zero-forcing number 11. The formalization verifies the exact graph and both numerical invariants, yielding an existential counterexample to the proposed bound Z(G) <= alpha(G) + 1 for connected graphs of maximum degree at most 3.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-09-20","reactions":{},"formalized":true,"formalizes":[{"title":"A counterexample to the zero forcing versus independence conjecture for cubic and subcubic graphs","identifier":"arXiv:2607.23664v1","relationship":"formalizes"}]}