1. On (r,g,χ)- graphs and cages of regularity r, girth g and chromatic number χGabriela Araujo-Pardo, Julio César Díaz-Calderón, Julián Fresán-Figueroa, Diego González-Moreno, Linda Lesniak, Mika Olsen, 2025, izvirni znanstveni članek Opis: For 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.
Ključne besede: graphs, cages, girth, chromatic number
Objavljeno v RUP: 03.11.2025; Ogledov: 390; Prenosov: 3
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