Arc-transitive cycle decompositions of tetravalent graphsMiklavič, Štefko (Avtor) Potočnik, Primož (Avtor) Wilson, Steve (Avtor) mathematicsgraph theorycycle decompositionautomorphism groupconsistent cyclemedial mapsA 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.20082013-10-15 12:09:20Delo ni kategorizirano3883ISSN: 0095-8956UDK: 519.17COBISS.SI-ID: 14627417sl