Abstract

An edge ranking of a graph is a restricted coloring of the edges with integers. It requires that every path between two edges with the same label i contains an intermediate edge with label j > i. An edge ranking is optimal if it uses the least number of distinct labels among all possible edge rankings. Recent research has revealed that the problem of finding an optimal edge ranking when restricted to trees admits a polynomial-time solution, yet the complexity of the problem for general graphs has remained open in the literature. In this paper, we prove that finding an optimal edge ranking of a graph is NP-hard. Also, we show that even finding a reasonably small edge ranking is infeasible in some cases.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.