Paths In Digraphs Research Articles

Longest paths in digraphs

In this paper, we give a sufficient condition on the degrees of the vertices of a digraph to insure the existence of a path of given length, and we characterize the extremal graphs.

On cycles and paths in digraphs

The purpose of this communication is to announce some sufficient conditions on degrees and number of arcs to insure the existence of cycles and paths in directed graphs. We show that these results are the best possible. The proofs of the theorems can be found in [4].

A Ramsey-type problem for paths in digraphs

A Ramsey-type problem for paths in digraphs

Enumeration of paths in digraphs

The solution of the problem of enumeration of then-paths in a digraph has so far been attempted through an indirect approach of enumerating the redundant chains. The approach has yielded an algorithm for determination of the general formula for the matrix of redundantn-chains and also a partial recurrence formula for the same. This paper presents a direct approach to the problem. It gives a recurrence relation expressing the matrix ofn-paths of a digraph in terms of the matrices of (n − 1)-paths of its first-order subgraphs. The result is exploited to give an algorithm for computing the matrix ofn-paths. The algorithm is illustrated with a 6 × 6 matrix.