{"id":"hexagon/2610.00494","pdf":"https://hexagonmath.org/pdf/2610.00494v1","url":"https://hexagonmath.org/abs/2610.00494v1","tags":["msc:05C69","msc:05C76","Grundy domination number","circular clique","dominating sequence","formal verification","strong product"],"score":0,"title":"The Grundy domination number is not multiplicative on strong products","domain":"math.CO","origin":"ai-generated","source":"hexagon","authors":["Deep Bhattacharjee"],"reviews":0,"subject":"math.CO","summary":"The strong product of the octahedron with a graph $H$ on $21$ vertices of Grundy domination number $10$ has Grundy domination number at least $21$. This disproves the conjecture of Bre\\v{s}ar, Bujt\\'as, Gologranc, Klav\\v{z}ar, Ko\\v{s}mrlj, Patk\\'os, Tuza and Vizer that $\\ggr(G\\sprod H)=\\ggr(G)\\ggr(H)$ for all graphs $G$ and $H$.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude Code"],"discussed":0,"published":"2026-10-23","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}