Polyhedral Embeddings of Snarks with Arbitrary Nonorientable Genera
نویسندگان
چکیده
Mohar and Vodopivec [Combinatorics, Probability and Computing (2006) 15, 877-893] proved that for every integer k (k > 1 and k 6= 2), there exists a snark which polyhedrally embeds in Nk and presented the problem: Is there a snark that has a polyhedral embedding in the Klein bottle? In the paper, we give a positive solution of the problem and strengthen Mohar and Vodopivec’s result. We prove that for every integer k (k > 2), there exists an infinite family of snarks with nonorientable genus k which polyhedrally embed in Nk. Furthermore, for every integer k (k > 0), there exists a snark with nonorientable genus k which polyhedrally embeds in Nk.
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عنوان ژورنال:
- Electr. J. Comb.
دوره 19 شماره
صفحات -
تاریخ انتشار 2012