We investigate vector chromatic number (χvec), Lovász θfunction of the complement (θ̄), and quantum chromatic number (χq) from the perspective of graph homomorphisms. We prove an analog of Sabidussi’s theorem for each of these parameters, i.e. that for each of the parameters, the value on the Cartesian product of graphs is equal to the maximum of the values on the factors. We also prove an analo...

In 1949 R. Frucht established that any finite group can be represented by a graph of degree three in the sense that automorphism group of the graph is isomorphic to the given group. In 1957 G. Sabidussi gave another step in this direction, proving that every finite group can be represented by an infinite number of regular graphs. The main result of this work is to give a proof of the Sabidussi’...

Let G be an eulerian graph. For each vertex v # V(G), let P(v) be a partition of the edges incident with v and set P= v # V(G) P(v), called a forbidden system of G. We say that P is admissible if |P & T | 2 |T | for every P # P and every edge cut T of G. H. Fleischner and A. Frank (1990, J. Combin. Theory Ser. B 50, 245 253) proved that if G is planar and P is any admissible forbidden system of...

The transport and technological cycles of unmanned aerial vehicles used in various options for the implementation agricultural technologies smart farming are discussed. analysis UAV function was carried out, starting with regular detailed photography ending spraying chemicals fields. It is shown that digitalization based on GERT-network models makes it possible to provide effective information ...

In the spring of ’99 my colleague Gert Smolka gave me a short introduction to constraint programming. During our discussion Gert emphasized that the search for efficient propagation algorithms leads to hard and well motivated questions in algorithmics. He pointed me to the papers [Reg94] by J.-C. Regin on “A filtering algorithm for constraints of difference in CSPs” and [GC97,GC00] by N. B. Gue...