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Our main interest lies in two different kinds of formal languages induced by the set of all self-avoiding walks on the graph starting at a given origin. The language of self-avoiding walks on a deterministically edge-labelled graph consists of all words obtained by reading along self-avoiding walks. We discuss that this language is regular or context-free, if and only if the given graph has ends of size at most 1 or 2, respectively.
Using tree-decomposition, thin ended graphs can be decomposed into finite parts. Configurations are appearances of self-avoiding walks on single parts, and compatible configurations on the composition tree correspond to self-avoiding walks on the original graph. By encoding compatible configurations as words we obtain the language of configurations. This language is context-free and thus the generating function of self-avoiding walks is algebraic.
|Number of pages||16|
|Journal||Internationale Mathematische Nachrichten|
|Publication status||Published - Aug 2020|
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
Fields of Expertise
- Information, Communication & Computing
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- 1 Active
Ebner, O., Lehner, F., Greinecker, F., Burkard, R., Wallner, J., Elsholtz, C., Woess, W., Raseta, M., Bazarova, A., Krenn, D., Lehner, F., Kang, M., Tichy, R., Sava-Huss, E., Klinz, B., Heuberger, C., Grabner, P., Barroero, F., Cuno, J., Kreso, D., Berkes, I. & Kerber, M.
1/05/10 → 30/06/24
Project: Research project