A short proof of Kotzig's theorem

TL;DR

This paper presents a concise proof of Kotzig's theorem on graphs with unique perfect matchings, and offers a new proof of Yeo's theorem using similar ideas, enhancing understanding of graph matchings.

Contribution

It provides a shorter, more direct proof of Kotzig's theorem and introduces a novel proof of Yeo's theorem based on the same conceptual framework.

Findings

Short proof of Kotzig's theorem

New proof of Yeo's theorem

Enhanced understanding of graph matchings

Abstract

A new shortest proof of Kotzig's Theorem about graphs with unique perfect matching is presented in this paper. It is well known that Kotzig's theorem is a consequence of Yeo's Theorem about edge-colored graph without alternating cycle. We present a proof of Yeo's Theorem based on the same ideas as our proof of Kotzig's theorem.