Special Hist-Snarks

TL;DR

This paper introduces new computer-generated Hist-snarks, generalizations of the Petersen graph, and discusses results on Hist-snarks supported by computational methods.

Contribution

It presents new Hist-snarks derived from computer algorithms and reports on related findings achieved with computational assistance.

Findings

New Hist-snarks generalizing Petersen graph

Computer-supported results on Hist-snarks

Enhanced understanding of Hist-snarks structure

Abstract

A Hist in a cubic graph $G$ is a spanning tree $T$ which has only vertices of degree three and one. A snark with a Hist is called a Hist-snark, see \cite{HO}. We present several computer generated Hist-snarks which form generalizations of the Petersen graph. Moreover, we state some results on Hist-snarks which have been achieved with computer support.