The n-ary first and second recursion theorems formalize two distinct, yet similar, notions of self-reference. Roughly, the n-ary first recursion theorem says that, for any n algo...
Let β(G), Γ(G) and IR(G) be the independence number, the upper domination number and the upper irredundance number, respectively. A graph G is called Γperfect if β(H) = Γ(H),...
We first prove that for any fixed k a cubic graph with few short cycles contains a Kk-minor. This is a direct generalisation of a result on girth by Thomassen. We then use this the...
Muchnik’s theorem about simple conditional descriptions states that for all strings a and b there exists a short program p transforming a to b that has the least possible length ...
Daniil Musatov, Andrei E. Romashchenko, Alexander ...
We prove that the max-cut and max-bisection problems are NP-hard on unit disk graphs. We also show that -precision graphs are planar for > 1/ 2 and give a dichotomy theorem f...