A counterexample to the lights out problem
János Nagy, Péter Pál Pach · Journal of Graph Theory · 2022
Abstract In this note we present a counterexample to the “lights out problem”, that is, for every odd prime we construct a simple graph with vertex set such that there does not exist elements such that for each . On the other hand, in the positive direction, we show that if a certain quadratic form is associated to the graph and the prime is positive definite, then the conjecture holds.