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Hyperbolic bridged graphs
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
2002 (English)In: European journal of combinatorics (Print), ISSN 0195-6698, E-ISSN 1095-9971, Vol. 23, no 6, p. 683-699Article in journal (Refereed) Published
Abstract [en]

Given a connected graph G, we take, as usual, the distance xy between any two vertices x, y of G to be the length of some geodesic between x and y. The graph G is said to be delta-hyperbolic, for some 3 : 0, if for all vertices x, y, u, v in G the inequality xy + uv :5 max{xu + yv, xv + yu} + delta holds, and G is bridged if it contains no finite isometric cycles of length four or more. In this paper, we will show that a finite connected bridged graph is 1-hyperbolic if and only if it does not contain any of a list of six graphs as an isometric subgraph.

Place, publisher, year, edition, pages
2002. Vol. 23, no 6, p. 683-699
Identifiers
URN: urn:nbn:se:miun:diva-13629DOI: 10.1006/eujc.2002.0591ISI: 000178136300005OAI: oai:DiVA.org:miun-13629DiVA, id: diva2:411798
Available from: 2011-04-19 Created: 2011-04-19 Last updated: 2025-09-25Bibliographically approved

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Moulton, Vincent

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