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  • On cyclic edge-connectivity of fullerenes
    Kutnar, Klavdija, 1980- ; Marušič, Dragan
    A graph is said to be cyclically ▫$k$▫-edge-connected, if at least ▫$k$▫ edges must be removed to disconnect it into two components, each containing a cycle. Such a set of ▫$k$▫ edges is called a ... cyclic-k-edge cutset and it is called a trivial cyclic-k-edge cutset if at least one of the resulting two components induces a single ▫$k$▫-cycle. It is known that fullerenes, that is, 3-connected cubic planar graphs all of whose faces are pentagons and hexagons, are cyclically 5-edge-connected. In this article it is shown that a fullerene ▫$F$▫ containing a nontrivial cyclic-5-edge cutset admits two antipodal pentacaps, that is, two antipodal pentagonal faces whose neighboring faces are also pentagonal. Moreover, it is shown that ▫$F$▫ has a Hamilton cycle, and as a consequence at least ▫$15 \cdot 2^{n/20-1/2}$▫ perfect matchings, where ▫$n$▫ is the order of ▫$F$▫.
    Vir: Discrete applied mathematics. - ISSN 0166-218X (Vol. 156, iss. 10, 2008, str. 1661-1669)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2008
    Jezik - angleški
    COBISS.SI-ID - 2017765

    Povezava(-e):

    http://dx.doi.org/10.1016/j.dam.2007.08.046
    Repozitorij Univerze na Primorskem - RUP
    DOI

vir: Discrete applied mathematics. - ISSN 0166-218X (Vol. 156, iss. 10, 2008, str. 1661-1669)
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