VSE knjižnice (vzajemna bibliografsko-kataložna baza podatkov COBIB.SI)
  • New results on bipartite biregular cages, block designs, and generalized polygons [Elektronski vir]
    Araujo-Pardo, Gabriela ; Kiss, György, matematik ; Szőnyi, Tamás
    In this paper, we obtain new lower and upper bounds for the problem of bipartite biregular cages. Moreover, for girth 6, we give the exact parameters of the (m, n; 6)- bipartite biregular cages when ... n ≡ −1 (mod m) using the existence of a Steiner system S(2, k = m, v = 1+n(m −1)+m). For girth g = 2r and r = {4, 6, 8}, we use results on t-good structures given by ovoids, spreads, and sub-polygons in generalized polygons to obtain (m, n; 2r)-bipartite biregular graphs. We emphasize that, as we improve the lower bounds on the order of these graphs, we also prove that some of them are (m, n; 2r)-bipartite biregular cages. In particular, we construct relatively small bipartite biregular graphs from a special class of generalized quadrangles and hexagons. In a special case, we show that the graph obtained is a (3, 4; 8)-bipartite biregular cage on 56 vertices. Note that the order of the smallest (3, 4; 8)-graph is 39
    Vir: Boletín de la Sociedad Matemática Mexicana. - ISSN 2296-4495 (Vol. 31, iss. 1, article no. 20, Mar. 2025, str. 1-17)
    Vrsta gradiva - e-članek
    Leto - 2025
    Jezik - angleški
    COBISS.SI-ID - 223994115

    Povezava(-e):

    https://link.springer.com/article/10.1007/s40590-024-00700-w
    DOI

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