Abstract
An n-bicirculant (in short, a bicirculant) is a graph admitting a non-identity automorphism having two cycles of equal length n in its cycle decomposition (called a (2,n)-semiregular automorphism). A graph is said to be symmetric if its automorphism group acts transitively on the set of its arcs. In this paper it is shown that a connected bicirculant X ≠ K 4 of prime valency admitting a group of automorphisms containing a (2,n)-semiregular automorphism and acting regularly on the set of arcs is near-bipartite (that is, with the chromatic number at most 3). Combining this result with the theory of Cayley maps new partial results are obtained in regards to the well-known conjecture that there are no snarks amongst Cayley graphs.
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Hujdurović, A., Kutnar, K., Marušič, D. (2013). On Prime-Valent Symmetric Bicirculants and Cayley Snarks. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2013. Lecture Notes in Computer Science, vol 8085. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40020-9_20
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DOI: https://doi.org/10.1007/978-3-642-40020-9_20
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