We show that for k ≥ 3 even the Ω(n) level of the Lasserre hierarchy cannot disprove a random k-CSP instance over any predicate type implied by k-XOR constraints, for example ...
Thomassen [9] conjectured that for all natural numbers k > 0 and m, every graph of minimum degree k + 1 contains a cycle of length congruent to 2m modulo k. We prove that this ...
We prove that the out-distance sequence {f+ (k)} of a vertex-transitive digraph of finite or infinite degree satisfies f+ (k + 1) f+ (k)2 for k 1, where f+ (k) denotes the numbe...
—It is investigated to what extent the trajectories of a stochastically switched (blinking) system follow the corresponding trajectories of the averaged system. Four cases have t...
We prove exponential lower bounds for the refutation of a random 3-CNF with linear number of clauses by k-DNF Resolution for k log n/ log log n. For this we design a specially ta...