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: Anais do X Encontro de Teoria da ComputaçãoDO - 10.5753/etc.2025.7019, 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.