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
Triangulated graphs and the elimination process
β Scribed by Donald J Rose
- Publisher
- Elsevier Science
- Year
- 1970
- Tongue
- English
- Weight
- 653 KB
- Volume
- 32
- Category
- Article
- ISSN
- 0022-247X
No coin nor oath required. For personal study only.
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,.
The wing-graph W (G) of a graph G has all edges of G as its vertices; two edges of G are adjacent in W (G) if they are the nonincident edges (called wings) of an induced path on four vertices in G. HoΓ ng conjectured that if W (G) has no induced cycle of odd length at least five, then G is perfect. A
## Abstract New characterizations of triangulated and cotriangulated graphs are presented. Cotriangulated graphs form a natural subclass of the class of strongly perfect graphs, and they are also characterized in terms of the shellability of some associated collection of sets. Finally, the notion o
## Abstract Given a set __F__ of digraphs, we say a graph __G__ is a __F__β__graph__ (resp., __F__\*β__graph__) if it has an orientation (resp., acyclic orientation) that has no induced subdigraphs isomorphic to any of the digraphs in __F__. It is proved that all the classes of graphs mentioned in