While finite cop-win finite graphs possess a good structural characterization, none is known for infinite cop-win graphs. As evidence that such a characterization might not exist, we provide as large as possible classes of infinite graphs with finite cop number. More precisely, for each infinite car
Mutation classes of diagrams via infinite graphs
β Scribed by Thilo Henrich
- Publisher
- John Wiley and Sons
- Year
- 2011
- Tongue
- English
- Weight
- 260 KB
- Volume
- 284
- Category
- Article
- ISSN
- 0025-584X
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β¦ Synopsis
Abstract
We give a complete description of the clusterβmutation classes of diagrams of Dynkin types \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathbb {A},\mathbb {B},\mathbb {D}$\end{document} and of affine Dynkin types \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathbb {B}^{(1)},\mathbb {C}^{(1)},\mathbb {D}^{(1)}$\end{document} via certain families of diagrams.
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