Isomorphism of chordal (6, 3) graphs

Isomorphisms ofP3-graphs

✍ Li, Xueliang 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 324 KB

For graphs G and G' with minimum degree at least 3 and satisfying one of three other conditions, w e prove that any isomorphism from the &graph P3(G) onto P3(G') can be induced by a (vertex-) isomorphism of G onto G'. This in some sense can be viewed as a counterpart with respect to P3-graphs for Wh

Centers of chordal graphs

✍ Gerard J. Chang 📂 Article 📅 1991 🏛 Springer Japan 🌐 English ⚖ 505 KB

P3-isomorphisms for graphs

✍ Aldred, R. E. L.; Ellingham, M. N.; Hemminger, R. L.; Jipsen, P. 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 204 KB

The P 3 -graph of a finite simple graph G is the graph whose vertices are the 3-vertex paths of G, with adjacency between two such paths whenever their union is a 4-vertex path or a 3-cycle. In this paper we show that connected finite simple graphs G and H with isomorphic P 3 -graphs are either isom

A generalization of chordal graphs

✍ P. D. Seymour; R. W. Weaver 📂 Article 📅 1984 🏛 John Wiley and Sons 🌐 English ⚖ 487 KB

In a 3-connected planar triangulation, every circuit of length 2 4 divides the rest of the edges into two nontrivial parts (inside and outside) which are "separated" by the circuit. Neil Robertson asked to what extent triangulations are characterized by this property, and conjectured an answer. In t

Vertex partitions of chordal graphs

✍ David R. Wood 📂 Article 📅 2006 🏛 John Wiley and Sons 🌐 English ⚖ 103 KB

## Abstract A __k‐tree__ is a chordal graph with no (__k__ + 2)‐clique. An ℓ‐__tree‐partition__ of a graph __G__ is a vertex partition of __G__ into ‘bags,’ such that contracting each bag to a single vertex gives an ℓ‐tree (after deleting loops and replacing parallel edges by a single edge). We pro

Chordal Completions of Planar Graphs

✍ F.R.K. Chung; D. Mumford 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 431 KB

We prove that every planar graph on \(n\) vertices is contained in a chordal graph with at most \(c n \log n\) edges for some abolsute constant \(c\) and this is best possible to within a constant factor. 1994 Academic Press, Inc.