Finding a biplanar imbedding of Cn×Cn×Cl×Pm

Joshua K. Lambert

Finding a biplanar imbedding of C_n×C_n×C_l×P_m

Joshua K. Lambert

Mathematical Sciences

Armstrong Atlantic State University

Research output: Contribution to journal › Article › peer-review

Abstract

Determining the biplanar crossing number of the graph C_n×C_n×C_l×P_mwas a problem proposed in a paper by Czabarka, Sykora, Szkely, and Vrto [2]. We find as a corollary to the main theorem of this paper that the biplanar crossing number of the aforementioned graph is zero. This result follows from the decomposition of C_n×C_n×C_l×P_m Pm into one copy of Cn2 x P|m, 2 copies of C_n×Pm, and a copy of _n×P2m.

Original language	English
Pages (from-to)	71-79
Number of pages	9
Journal	Ars Combinatoria
Volume	121
State	Published - 2015

Scopus Subject Areas

General Mathematics

Cite this

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title = "Finding a biplanar imbedding of Cn×Cn×Cl×Pm",

abstract = "Determining the biplanar crossing number of the graph Cn×Cn×Cl×Pmwas a problem proposed in a paper by Czabarka, Sykora, Szkely, and Vrto [2]. We find as a corollary to the main theorem of this paper that the biplanar crossing number of the aforementioned graph is zero. This result follows from the decomposition of Cn×Cn×Cl×Pm Pm into one copy of Cn2 x P|m, 2 copies of Cn×Pm, and a copy of n×P2m.",

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AB - Determining the biplanar crossing number of the graph Cn×Cn×Cl×Pmwas a problem proposed in a paper by Czabarka, Sykora, Szkely, and Vrto [2]. We find as a corollary to the main theorem of this paper that the biplanar crossing number of the aforementioned graph is zero. This result follows from the decomposition of Cn×Cn×Cl×Pm Pm into one copy of Cn2 x P|m, 2 copies of Cn×Pm, and a copy of n×P2m.

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Finding a biplanar imbedding of C_n×C_n×C_l×P_m

Abstract

Scopus Subject Areas

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