On $k$-transitive closures of directed paths

TL;DR

This paper investigates the structure and properties of $k$-transitive closures of directed paths, extending the concept of transitive orientations in graphs to a more general setting.

Contribution

It introduces and analyzes the properties of $k$-transitive orientations, generalizing traditional transitive orientations of graphs.

Findings

Characterization of $k$-transitive closures of directed paths

Formulation of properties of $k$-transitive orientations

Extension of transitive orientation concepts

Abstract

In this paper we study the structure of $k$-transitive closures of directed paths and formulate several properties. Concept of $k$-transitive orientation generalize the traditional concept of transitive orientation of a graph.