| Title: | Arc-transitive cycle decompositions of tetravalent graphs |
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| Authors: | ID Miklavič, Štefko (Author)
ID Potočnik, Primož (Author)
ID Wilson, Steve (Author) |
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| Files: |  http://dx.doi.org/10.1016/j.jctb.2008.01.005
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| Language: | English |
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| Work type: | Not categorized |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | IAM - Andrej Marušič Institute
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| Abstract: | 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. |
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| Keywords: | mathematics, graph theory, cycle decomposition, automorphism group, consistent cycle, medial maps |
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| Year of publishing: | 2008 |
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| Number of pages: | str. 1181-1192 |
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| Numbering: | Vol. 98, no. 6 |
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| PID: | 20.500.12556/RUP-3883  |
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| ISSN: | 0095-8956 |
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| UDC: | 519.17 |
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| COBISS.SI-ID: | 14627417 |
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| Publication date in RUP: | 15.10.2013 |
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| Views: | 6594 |
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| Downloads: | 91 |
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