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Mathematical Communications, Vol. 9 No. 1, 2004.

Original scientific paper

Blanuša double

A. Orbanić
T. Pisanski
M. Randić
B. Servatius

Full text: english pdf 831 Kb

page 91-103

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Abstract

A snark is a non-trivial cubic graph admitting no Tait coloring.
We examine the structure of the two known snarks on 18 vertices, the Blanuša graph and the Blanuša double. By showing that one is of genus 1, the other of genus 2, we obtain maps on the torus and double torus which are not 4-colorable.
The Blanuša graphs appear also to be a counter example for the
conjecture that the orientable genus of a dot product of n Petersen graphs is n-1 (Tinsley and Watkins, 1985).
We also prove that the 6 known snarks of order 20 are all of genus 2.

Keywords

Blanuša snark; Blanuša double snark; dot product; embeddings

Hrčak ID:

720

URI

https://hrcak.srce.hr/720

Publication date:

26.6.2004.

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