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2012 | 32 | 1 | 91-108
Tytuł artykułu

The projective plane crossing number of the circulant graph C(3k;{1,k})

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper we prove that the projective plane crossing number of the circulant graph C(3k;{1,k}) is k-1 for k ≥ 4, and is 1 for k = 3.
Słowa kluczowe
Wydawca
Rocznik
Tom
32
Numer
1
Strony
91-108
Opis fizyczny
Daty
wydano
2012
otrzymano
2010-09-02
poprawiono
2011-01-26
zaakceptowano
2011-01-26
Twórcy
autor
  • Department of Mathematics, Sogang University, Seoul 121-742, Korea
Bibliografia
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  • [5] R.K. Guy, T. Jenkyns and J. Schaer, The toroidal crossing number of the complete graph, J. Combin. Theory 4 (1968) 376-390, doi: 10.1016/S0021-9800(68)80063-8.
  • [6] P. Hliněný, Crossing number is hard for cubic graphs, J. Combin. Theory (B) 96 (2006) 455-471, doi: 10.1016/j.jctb.2005.09.009.
  • [7] P.T. Ho, A proof of the crossing number of $K_{3,n}$ in a surface, Discuss. Math. Graph Theory 27 (2007) 549-551, doi: 10.7151/dmgt.1379.
  • [8] P.T. Ho, The crossing number of C(3k+1;{1,k}), Discrete Math. 307 (2007) 2771-2774, doi: 10.1016/j.disc.2007.02.001.
  • [9] P.T. Ho, The crossing number of $K_{4,n}$ on the projective plane, Discrete Math. 304 (2005) 23-34, doi: 10.1016/j.disc.2005.09.010.
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  • [13] X. Lin, Y. Yang, J. Lu and X. Hao, The crossing number of C(n;{1,⌊ n/2⌋-1}), Util. Math. 71 (2006) 245-255.
  • [14] D. Ma, H. Ren and J. Lu, The crossing number of the circular graph C(2m+2,m), Discrete Math. 304 (2005) 88-93, doi: 10.1016/j.disc.2005.04.018.
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  • [21] L.A. Székely, A successful concept for measuring non-planarity of graphs: the crossing number, Discrete Math. 276 (2004) 331-352, doi: 10.1016/S0012-365X(03)00317-0.
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Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1588
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