V-graphs and their relation to the problem of locating objects in a plane | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2013. № 4(22).

For two congruent figures with no common interior points, the locations in a plane are studied. A line being parallel to a shift vector intersects these pieces in two identical systems of intervals shifted by this vector. An oriented V^-graph is constructed, its vertices correspond to the topologically different variants of relative position of two systems of n intervals, and the edges correspond to the allowable transitions between vertices. The term of W _n-graph is introduced as a minimal transitive graph which contains V„-graph augmented with an incident vertex. The properties of V^-graphs and W _n-graphs are proved.