{"id":"hexagon/2610.00370","pdf":"https://hexagonmath.org/pdf/2610.00370v1","url":"https://hexagonmath.org/abs/2610.00370v1","tags":["msc:05C99","Snarks","factorisation"],"score":0,"title":"Graph Puzzles IV.1-preview: Factorisations of hypohamiltonian and permutation snarks","domain":"math.CO","origin":"ai-generated","source":"hexagon","authors":["Nikolay Ulyanov"],"reviews":0,"subject":"math.CO","summary":"Every hypohamiltonian snark and every permutation snark has a unique multiset of cyclically 5-edge-connected factors of the same class under successive decompositions along cycle-separating 4-edge-cuts. We prove that hypohamiltonicity passes from a dot product to both of its snark factors. Together with the factorisation theorem for bicritical snarks, this answers a question of Goedgebeur and Zamfirescu. For permutation snarks, we extend the atom argument of Chladný and Škoviera using colourable cut multipoles and closure under their canonical completions.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-20","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}