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  • Characterizing 2-crossing-critical graphs [Elektronski vir]
    Bokal, Drago, 1978- ...
    It is very well-known that there are precisely two minimal non-planar graphs: ▫$K_5$▫ and ▫$K_{3,3}$▫ (degree 2 vertices being irrelevant in this context). In the language of crossing numbers, these ... are the only 1-crossing-critical graphs: they each have crossing number at least one, and every proper subgraph has crossing number less than one. In 1987, Kochol exhibited an infinite family of 3-connected, simple 2-crossing-critical graphs. In this work, we: (i) determine all the 3-connected 2-crossing-critical graphs that contain a subdivision of the Möbius Ladder ▫$V_{10}$▫; (ii) show how to obtain all the not 3-connected 2-crossing-critical graphs from the 3-connected ones; (iii) show that there are only finitely many 3-connected 2-crossing-critical graphs not containing a subdivision of ▫$V_{10}$▫; and (iv) determine all the 3-connected 2-crossing-critical graphs that do not contain a subdivision of ▫$V_{8}$▫.
    Vrsta gradiva - znanstvena monografija ; neleposlovje za odrasle
    Založništvo in izdelava - Ljubljana : IMFM, 2013
    Jezik - angleški
    COBISS.SI-ID - 16809049

    Povezava(-e):

    http://www.imfm.si/preprinti/PDF/01193.pdf

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