Modulus of edge covers and stars

TL;DR

This paper investigates the discrete p-modulus of edge covers in graphs, establishing bounds and efficient computation methods through duality with fractional edge covers and stars.

Contribution

It introduces bounds and efficient computation techniques for the modulus of edge covers, linking it to fractional covers and star families.

Findings

Bounds on edge cover modulus are established.

Efficient algorithms for computing the modulus are proposed.

The relationship between edge covers, fractional covers, and stars is clarified.

Abstract

This paper explores the modulus (discrete $p$-modulus) of the family of edge covers on a discrete graph. This modulus is closely related to that of the larger family of fractional edge covers; the modulus of the latter family is guaranteed to approximate the modulus of the former within a multiplicative factor. The bounds on edge cover modulus can be computed efficiently using a duality result that relates the fractional edge covers to the family of stars.