An infinite family of Type 2 snarks with small girth obtained by Kochol’s Superposition
Open Access
- 20 July 2025
- conference paper
- Published by Sociedade Brasileira de Computação
- p. 1-5
Abstract
Snarks are cubic graphs with peculiar properties, making them relevant to several problems in graph theory, such as edge and total coloring. While infinite families of Type 1 snarks are well known, Type 2 snarks remain rare and difficult to construct. In 1996, Kochol introduced a method for constructing new snarks by combining two known snarks, usually Type 1. We apply Kochol’s superposition to obtain new Type 2 snarks. As a result, we construct an infinite family of Type 2 snarks with girth 4 by Kochol’s superposition of a known Type 2 snark with the infinite family of Goldberg snarks.Keywords
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