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  • 2-cell embeddings with prescribed face lengths and genus [Elektronski vir]
    Mohar, Bojan, 1956-
    Let ▫$n$▫ be a positive integer, let ▫$d_1,...,d_n$▫ be a sequence of positive integers, and let ▫$q = \frac{1}{2} \sum_{i=1}^n d_i$▫. It is shown that there exists a connected graph ▫$G$▫ of order ... ▫$n$▫, whose degree sequence is ▫$d_1,..., dn$▫ and such that ▫$G$▫ admits a 2-cell embedding in every closed surface whose Euler characteristic is at least ▫$n-q+1$▫, if and only if ▫$q$▫ is an integer and ▫$q \ge n-1$▫. Moreover, the graph ▫$G$▫ is loopless if and only if ▫$d_i \le q$▫ for ▫$i=1,...,n$▫ This, in particular, answers a question of Arkadiy Skopenkov.
    Vir: Preprint series. - ISSN 1318-4865 (Vol. 45, št. 1037, 2007, str. 1-9)
    Vrsta gradiva - e-članek
    Leto - 2007
    Jezik - angleški
    COBISS.SI-ID - 14783065

    Povezava(-e):

    http://www.imfm.si/preprinti/PDF/01037.pdf

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