On cyclic edge-connectivity of fullerenes |
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Authors: | Klavdija Kutnar,Dragan Maru&scaron i? |
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Affiliation: | a University of Primorska, FAMNIT, Glagoljaška 8, 6000 Koper, Slovenia b University of Ljubljana, IMFM, Jadranska 19, 1000 Ljubljana, Slovenia |
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Abstract: | 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 15·2n/20-1/2 perfect matchings, where n is the order of F. |
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Keywords: | Graph Fullerene graph Cyclic edge-connectivity Hamilton cycle Perfect matching |
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