Snarks from a Kaszonyi perspective: a survey

TL;DR

This survey reviews a collection of results and open problems related to snarks, special cubic graphs that cannot be edge-colored with three colors, based on Kaszonyi's early 1970s work, aiming to inspire further research.

Contribution

It compiles and explains Kaszonyi's foundational results and open problems on snarks, making them accessible for new researchers and students.

Findings

Summarizes key results on snarks from Kaszonyi's work.

Identifies open problems suitable for undergraduate research.

Provides a foundation for future investigations into snarks.

Abstract

This is a survey or exposition of a particular collection of results and open problems involving snarks --- simple "cubic" (3-valent) graphs for which, for nontrivial reasons, the edges cannot be 3-colored. The results and problems here are rooted in a series of papers by Laszlo Kaszonyi that were published in the early 1970s. The problems posed in this survey paper can be tackled without too much specialized mathematical preparation, and in particular seem well suited for interested undergraduate mathematics students to pursue as independent research projects. This survey paper is intended to facilitate research on these problems.