An infinite family of Type 2 snarks with small girth obtained by Kochol’s Superposition - Araújo, Rieli; Figueiredo, Celina M. H. de; Sasaki, Diana; Dantas, Simone (Anais do Encontro de Teoria da Computação (ETC), 2025)
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.