| Title: | Arc-transitive cycle decompositions of tetravalent graphs |
|---|
| Authors: | ID Miklavič, Štefko (Author)
ID Potočnik, Primož (Author)
ID Wilson, Steve (Author) |
|---|
| Files: |  http://dx.doi.org/10.1016/j.jctb.2008.01.005
|
|---|
| Language: | English |
|---|
| Work type: | Not categorized |
|---|
| Typology: | 1.01 - Original Scientific Article |
|---|
| Organization: | IAM - Andrej Marušič Institute
|
|---|
| 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. |
|---|
| Keywords: | mathematics, graph theory, cycle decomposition, automorphism group, consistent cycle, medial maps |
|---|
| Year of publishing: | 2008 |
|---|
| Number of pages: | str. 1181-1192 |
|---|
| Numbering: | Vol. 98, no. 6 |
|---|
| PID: | 20.500.12556/RUP-3883  |
|---|
| ISSN: | 0095-8956 |
|---|
| UDC: | 519.17 |
|---|
| COBISS.SI-ID: | 14627417 |
|---|
| Publication date in RUP: | 15.10.2013 |
|---|
| Views: | 4327 |
|---|
| Downloads: | 86 |
|---|
| Metadata: |    |
|---|
|
:
|
Copy citation |
|---|
| | | | Average score: | (0 votes) |
|---|
| Your score: | Voting is allowed only for logged in users. |
|---|
| Share: |  |
|---|
Hover the mouse pointer over a document title to show the abstract or click
on the title to get all document metadata. |
