Monochromatic s-t Paths in Edge-Colored Graphs

In this paper we consider an approach to solve the problem of finding monochromatic s-t paths in edge-colored graphs. This approach is based on constructing logical models for the problem. Algorithmic problems extensively investigated in bioinformatics (see e.g. [1] – [3]). In particular, there are a number of applications of different problems of finding paths. In this paper we consider the problem of finding monochro-matic s-t paths in edge-colored graphs. A graph G = (V, E) is the set of nodes V connected by edges from the set E. We assume that each edge of a graph has a color. All graphs considered are finite and have no loops. If the number of colors is restricted by an integer c, we speak about c-edge-colored graphs. In this paper, we consider only simple paths. Two paths in a graph are said to be edge-disjoint if they do not share any common edge. The problem of finding monochromatic s-t paths in edge-colored graphs (2MP): Instance: A c-edge-colored graph G = (V, E) with c ≥ 2, s, t ∈ V .