Kirszbraun extension on connected finite graph

TL;DR

This paper proves the Kirszbraun extension property on connected finite graphs, establishes its uniqueness in real-valued cases, and provides an efficient polynomial-time algorithm for its computation.

Contribution

It demonstrates that the tight function is a Kirszbraun extension, proves uniqueness in real-valued cases, and introduces a polynomial-time algorithm for calculation.

Findings

The tight function is a Kirszbraun extension.

Uniqueness of Kirszbraun extension in real-valued case.

Efficient polynomial-time algorithm for extension calculation.

Abstract

We prove that the tight function introduced Sheffield and Smart (2012) is a Kirszbraun extension. In the real-valued case we prove that Kirszbraun extension is unique. Moreover, we produce a simple algorithm which calculates efficiently the value of Kirszbraun extension in polynomial time.