Compatible connectedness in graphs and topological spaces
| Autor: | Richard G. Wilson, Victor Neumann-Lara |
|---|---|
| Rok vydání: | 1995 |
| Předmět: |
Discrete mathematics
Algebra and Number Theory Comparability graph law.invention Modular decomposition Combinatorics Computational Theory and Mathematics law Line graph Topological graph theory Cograph Geometry and Topology Mathematics Universal graph Distance-hereditary graph Forbidden graph characterization |
| Zdroj: | Order. 12:77-90 |
| ISSN: | 1572-9273 0167-8094 |
| Popis: | A topology on the vertex set of a graphG iscompatible with the graph if every induced subgraph ofG is connected if and only if its vertex set is topologically connected. In the case of locally finite graphs with a finite number of components, it was shown in [11] that a compatible topology exists if and only if the graph is a comparability graph and that all such topologies are Alexandroff. The main results of Section 1 extend these results to a much wider class of graphs. In Section 2, we obtain sufficient conditions on a graph under which all the compatible topologies are Alexandroff and in the case of bipartite graphs we show that this condition is also necessary. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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