This paper deals with the problem of constructing directed trees of optimal weight and root with depth at most (||) (called – ). We first prove that the maximization and the minimization versions are equal-approximable under the that measures how the value of an approximate solution is placed...

A dual-Eulerian graph is a plane graph which has an ordering defined on its edge set which forms simultaneously an Euler circuit in the graph and an Euler circuit in the dual graph. Dual-Eulerian graphs were defined and studied in the context of silicon optimization of cmos layouts. They are...

The possibilities for circuits of length 4 to appear together in a cubic bigraph are classified. That has consequences on the structure of minimally 1-factorable regular bigraphs, i.e. those in which each 1-factor lies in precisely one 1-factorization. We characterize minimally 1-factorable...

We define an between finite simple graphs and use it to define an equivalence relation on the set of natural numbers. The least integers of the equivalence classes serve as canonical code numbers for graphs and this new integer sequence we call the sequence of Characterizations of the...

A new approach to the problem is presented. The difficulty of the problem is characterized by the existence of two kinds of chaining processes. A conjecture claiming that the two examined chaining are the only possible is formulated. Should such conjecture be true, the approach could be...

We propose a new graph metric and study its properties. In contrast to the standard geodesic distance in connected graphs, it takes into account all paths between vertices. Simple formulas for the increments of forest distances under basic transformations of a weighted multigraph are presented...

The labeling problem considered for this is called face-labeling of the maximal planar or triangular planar graphs in connection with the notion of the . Several triangular planar and maximal planar graphs such as the wheels, the fans etc. have been considered. The face-labeling of maximal...

Given a set of points in a plane, a spanning tree is a set of edges that connects all the points and contains no cycles. If each edge is weighted using the rectilinear distance metric, the rectilinear minimum spanning tree is a tree whose sum of edge weights is minimum. A naive approach to...

This paper is concerned with the stochastic shortest path problem with recourse when limited forms of spatial and temporal arc cost dependencies are accounted for. Recourse is defined as the opportunity for a decision-maker to re-evaluate his or her remaining path when en route information is...