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: 295; Prenosov: 2
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2. A note on girth-diameter cagesGabriela Araujo-Pardo, Marston D. E. Conder, Natalia García-Colín, György Kiss, Dimitri Leemans, 2025, izvirni znanstveni članek Opis: In this paper we introduce a problem closely related to the Cage Problem and the Degree Diameter Problem. For integers k ≥ 2, g ≥ 3 and d ≥ 1, we define a (k; g, d)-graph to be a k-regular graph with girth g and diameter d. We denote by n₀(k; g, d) the smallest possible order of such a graph, and, if such a graph exists, we call it a (k; g, d)-cage. In particular, we focus on (k; 5, 4)-graphs. We show that n₀(k; 5, 4) ≥ k² + k + 2 for all k, and report on the determination of all (k; 5, 4)-cages for k = 3, 4 and 5 and of examples with k = 6, and describe some examples of (k; 5, 4)-graphs which prove that n₀(k; 5, 4) ≤ 2k² for infinitely many k.
Ključne besede: cages, girth, degree-diameter problem
Objavljeno v RUP: 10.06.2025; Ogledov: 707; Prenosov: 15
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4. O ekstremnih grafih z dano stopnjo in premerom/ožino : doktorska disertacijaSlobodan Filipovski, 2018, doktorska disertacija Ključne besede: adjacency matrix, antipodal graphs, cages, excess, defect, Ramanujan graphs, selfrepeats, degree/diameter problem, spectrum, Moore graphs, asymptotic density, distance matrices, Bermond and Bollobas problem
Objavljeno v RUP: 21.01.2019; Ogledov: 5249; Prenosov: 0 |
