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Title: Arc-transitive cycle decompositions of tetravalent graphs Miklavič, Štefko (Author)Potočnik, Primož (Author)Wilson, Stephen (Author) http://dx.doi.org/10.1016/j.jctb.2008.01.005 English Not categorized 1.01 - Original Scientific Article IAM - Andrej Marušič Institute A cycle decomposition of a graph ▫$\Gamma$▫ is a set ▫$\mathcal{C}$▫ of cycles of ▫$\Gamma$▫ such that every edge of ▫$\Gamma$▫ belongs to exactly one cycle in ▫$\mathcal{C}$▫. Such a decomposition is called arc-transitive if the group of automorphisms of ▫$\Gamma$▫ that preserve setwise acts transitively on the arcs of ▫$\Gamma$▫. In this paper, we study arc-transitive cycle decompositions of tetravalent graphs. In particular, we are interested in determining and enumerating arc-transitive cycle decompositions admitted by a given arc-transitive tetravalent graph. Among other results we show that a connected tetravalent arc-transitive graph is either 2-arc-transitive, or is isomorphic to the medial graph of a reflexible map, or admits exactly one cycle structure. mathematics, graph theory, cycle decomposition, automorphism group, consistent cycle, medial maps 2008 str. 1181-1192 Vol. 98, no. 6 0095-8956 519.17 14627417 1489 53 Document is not linked to any category.

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## Secondary language

Language: English matematika, teorija grafov, dekompozicija ciklov, grupa avtomorfizmov