For any partition of {1, 2, . . . , n} we define its increments Xi, 1 i n by Xi = 1 if i is the smallest element in the partition block that contains it, Xi = 0 otherwise. We pr...
Abstract. Let the graph G = (V, E) be a cycle with n + 1 vertices, nonnegative vertex weights and positive edge lengths. The inverse 1-median problem on a cycle consists in changin...
Rainer E. Burkard, Carmen Pleschiutschnig, Jianzho...
We introduce a new graph for all whose cartesian powers the vertex isoperimetric problem has nested solutions. This is the fourth kind of graphs with this property besides the wel...
A general (rectangular) partition is a partition of a rectangle into an arbitrary number of non-overlapping subrectangles. This paper examines vertex colorings using four colors o...
The communities of a social network are sets of vertices with more connections inside the set than outside. We theoretically demonstrate that two commonly observed properties of s...