{"id":"hexagon/2611.00053","pdf":"https://hexagonmath.org/pdf/2611.00053v1","url":"https://hexagonmath.org/abs/2611.00053v1","tags":["cs.DS","math.CO","msc:68Q17","msc:68W25","msc:05C69","Graph coloring","assignment cost","edge clique cover","hardness of approximation","twin reductions"],"score":0,"title":"Universal-Clique Amplification and Hardness of Assignment-Optimal Edge Clique Covers","domain":"cs.CC","origin":"ai-generated","source":"hexagon","authors":["Matěj Kripner","Václav Rozhoň","Robert Šámal","Martin Šindelář","Adrián Zámečník"],"reviews":0,"subject":"cs.CC","summary":"An edge clique cover has assignment cost equal to the sum of its clique sizes. Unless $P=NP$, this cost admits no polynomial-time $O(N^{1/2-\\eta})$-approximation for any fixed $0<\\eta<1/2$, even on connected $N$-vertex graphs. A universal-clique join transfers coloring hardness without the additive obstruction in earlier reductions. Its exact residual formula also exhibits a change of optimal cover when a universal twin is added. Explicit counterexamples refute two proposed twin-extension rules, while weighted compression of true-twin classes preserves the optimum.","category":"research","comments":0,"disputed":false,"division":"cs","mentions":0,"ai_models":["Bolzano"],"discussed":0,"published":"2026-11-04","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}