Quantum optics experiments contribute to a deeper understanding of quantum theory. Neutron phase-echo and spin rotation experiments have shown that, in all cases of an interaction, parasitic beams are produced which cannot be recombined with the original beam in an ideal way. This means that a complete reconstruction of the original state would, in principle, be impossible. Thus a kind of intri...

Unavoidable subgraphs have been widely studied in the context of Ramsey Theory. The research in this area focuses on highly structured graphs such as cliques, cycles, paths, stars, trees, and wheels. We propose to study maximum unavoidable subgraphs measuring the size in the number of edges. We computed maximum unavoidable subgraphs for graphs up to order nine via SAT solving and observed that ...

We show that every complete n-vertex simple topological graph contains a subgraph on at least $$(\log n)^{1/4 - o(1)}$$ vertices is weakly isomorphic to the convex geometric or twisted graph. This first improvement bound $$\varOmega (\log ^{1/8}n)$$ obtained in 2003 by Pach, Solymosi, and Tóth. also plane path of length n)^{1 -o(1)}$$ .