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Locally bounded coverings and factorial properties of graphs
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Lozin, Vadim V., Mayhill, Colin and Zamaraev, Victor. (2012) Locally bounded coverings and factorial properties of graphs. European Journal of Combinatorics, Vol.33 (No.4). pp. 534-543. ISSN 0195-6698
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Official URL: http://dx.doi.org/10.1016/j.ejc.2011.10.006
Abstract
For a graph property X, let Xn be the number of graphs with vertex set {1,…,n} having property X, also known as the speed of X. A property X is called factorial if X is hereditary (i.e. closed under taking induced subgraphs) and nc1n≤Xn≤nc2n for some constants c1 and c2. Hereditary properties with speed slower than factorial are surprisingly well structured. The situation with factorial properties is more complicated and less explored. Only the properties with speeds up to the Bell number are well studied and well behaved. To better understand the behavior of factorial properties with faster speeds we introduce a structural tool called locally bounded coverings and show that a variety of graph properties can be described by means of this tool.
| Item Type: | Journal Article |
|---|---|
| Divisions: | Faculty of Science > Mathematics |
| Journal or Publication Title: | European Journal of Combinatorics |
| Publisher: | Academic Press |
| ISSN: | 0195-6698 |
| Date: | 2012 |
| Volume: | Vol.33 |
| Number: | No.4 |
| Page Range: | pp. 534-543 |
| Identification Number: | 10.1016/j.ejc.2011.10.006 |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Access rights to Published version: | Restricted or Subscription Access |
| URI: | http://wrap.warwick.ac.uk/id/eprint/48960 |
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