A Simple Proof of the F{\'a}ry-Wagner Theorem

TL;DR

This paper presents a straightforward proof of the F{á}ry-Wagner theorem, establishing that every planar graph can be drawn with straight-line edges, simplifying previous proofs and enhancing understanding of planar graph drawings.

Contribution

The paper provides a simplified, accessible proof of a fundamental theorem in graph theory, improving clarity and pedagogical value.

Findings

Every plane graph admits a straight-line drawing.

The proof simplifies understanding of planar graph embeddings.

Supports further research in graph drawing algorithms.

Abstract

We give a simple proof of the following fundamental result independently due to Fary (1948) and Wagner (1936): Every plane graph has a drawing in which every edge is straight.