On (r,g,χ)- graphs and cages of regularity r, girth g and chromatic number χAraujo-Pardo, Gabriela (Avtor) Díaz-Calderón, Julio César (Avtor) Fresán-Figueroa, Julián (Avtor) González-Moreno, Diego (Avtor) Lesniak, Linda (Avtor) Olsen, Mika (Avtor) graphscagesgirthchromatic numberFor integers r ≥ 2, g ≥ 3 and χ ≥ 2, an (r, g, χ)-graph is an r-regular graph with girth g and chromatic number χ. Such a graph of minimum order is called an (r, g, χ)-cage. Here we prove the existence of (r, g, χ)-graphs for all r and even g when χ = 2 and for all r and g when χ = 3. Furthermore, using both existence proofs and explicit constructions we give examples of (r, g, χ)-graphs for infinitely many values of r, g, χ.Založba Univerze na Primorskem20252025-11-03 12:46:40Članek v reviji22079UDK: 519.17eISSN: 2590-9770DOI: 10.26493/2590-9770.1737.0f8sl