The main theorem of this paper gives a forbidden induced subgraph condition on G that is sufficient for chordality of G m . This theorem is a generalization of a theorem of Balakrishnan and Paulraja who had provided this only for m = 2. We also give a forbidden subgraph condition on G that is suffi
On powers and centers of chordal graphs
β Scribed by Renu Laskar; Douglas Shier
- Publisher
- Elsevier Science
- Year
- 1983
- Tongue
- English
- Weight
- 486 KB
- Volume
- 6
- Category
- Article
- ISSN
- 0166-218X
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For an undirected graph G the kth power G k of G is the graph with the same vertex set as G where two vertices are adjacent iff their distance is at most k in G. In this paper we prove that any LexBFS-ordering of a chordal graph is a common perfect elimination ordering of all odd powers of this grap
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
## Abstract The __chordality__ of a graph __G__ = (__V, E__) is defined as the minimum __k__ such that we can write __E__ = __E__~1~ β© β¦ β© __E__~__k__~ with each (__V, E__~__i__~) a chordal graph. We present several results bounding the value of this generalization of boxicity. Our principal result