We show that a graph is weakly triangulated, or weakly chordal, if and only if it can be generated by starting with a graph with no edges, and repeatedly adding an edge, so that the new edge is not the middle edge of any chordless path with four vertices. This is a corollary of results due to Sritha
Recognizing quasi-triangulated graphs
β Scribed by Jeremy P Spinrad
- Publisher
- Elsevier Science
- Year
- 2004
- Tongue
- English
- Weight
- 206 KB
- Volume
- 138
- Category
- Article
- ISSN
- 0166-218X
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β¦ Synopsis
This paper discusses a method for recognizing certain graph classes based on elimination schemes more e ciently. We reduce the time bound for recognizing quasi-triangulated graphs from O(n 3 ) to O(n 2:77 ), and perfect elimination bipartite and cop-win graphs from O(n 3 ) to O(n 3 =log n).
π SIMILAR VOLUMES
A graph G is called triangulated (or rigid-circuit graph, or chordal graph) if every circuit of G with length greater than 3 has a chord. It can be shown (see, UI, . . . , u,, . Let G = G,.
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