## Abstract We define two types of bipartite graphs, chordal bipartite graphs and perfect elimination bipartite graphs, and prove theorems analogous to those of Dirac and Rose for chordal graphs (rigid circuit graphs, triangulated graphs). Our results are applicable to Gaussian elimination on spars
On b-perfect Chordal Graphs
✍ Scribed by Frédéric Maffray; Meriem Mechebbek
- Publisher
- Springer Japan
- Year
- 2009
- Tongue
- English
- Weight
- 228 KB
- Volume
- 25
- Category
- Article
- ISSN
- 0911-0119
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📜 SIMILAR VOLUMES
Let G = (V,E) be a finite undirected connected graph. We show that there is a common perfect elimination ordering of all powers of G which represent chordal graphs. Consequently, if G and all of its powers are chordal then all these graphs admit a common perfect elimination ordering. Such an orderin
A graph is called equistable when there is a non-negative weight function on its vertices such that a set S of vertices has total weight 1 if and only if S is maximal stable. We show that a chordal graph is equistable if and only if every two adjacent non-simplicial vertices have a common simplicial