𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A characterization of k-trees

✍ Scribed by Ralf Fröberg

Publisher
Elsevier Science
Year
1992
Tongue
English
Weight
147 KB
Volume
104
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

✦ Synopsis

The purpose of this note is to give a local criterion for a graph to be a k-tree. We show that a connected graph with the right number of edges is a k-tree if and only if the neighbourhood of each vertex is a (k -l)-tree.

📜 SIMILAR VOLUMES

On simple characterizations of k-trees
On simple characterizations of k-trees
✍ Donald J. Rose 📂 Article 📅 1974 🏛 Elsevier Science 🌐 English ⚖ 422 KB

k-trees are I special class of perfect elimination grap% which arise in the study of sparse linear systems. We present four simple ch,&r.xterizations of k-trees involving cliques, paths, and separators.

A characterization of bivariegated trees
A characterization of bivariegated trees
✍ A.R. Bednarek; E.L. Sanders 📂 Article 📅 1973 🏛 Elsevier Science 🌐 English ⚖ 938 KB

A @mph ix biwwiepted PO itr vertca; Jiet c"8n be partitioned into two equal sets such that e&t WPWQ is od@tuxnt to me and only one vertex in the set not containing it. A tree with 2~ verlh & bivaticgatcd Of an," mly if the largest indcpcndcnt subset of the vertex set hw uxdind n. A constructive desc

A characterization of (γ, i)-trees
A characterization of (γ, i)-trees
✍ E. J. Cockayne; O. Favaron; C. M. Mynhardt; J. Puech 📂 Article 📅 2000 🏛 John Wiley and Sons 🌐 English ⚖ 170 KB
Enumerating k-trees
Enumerating k-trees
✍ Dominique Foata 📂 Article 📅 1971 🏛 Elsevier Science 🌐 English ⚖ 256 KB

AMUacL k functtonal dicf~mition of rooted k-trees is given, enabling k-trees with n labeled points m be enumerated without any calculation.

Algorithms for a Core and k-Tree Core of
Algorithms for a Core and k-Tree Core of a Tree
✍ S.T. Peng; A.B. Stephens; Y. Yesha 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 595 KB

We first give a one-pass algorithm for finding the core of a tree. This algorithm is a refinement of the two-pass algorithm of Morgan and Slater. We then define a generalization of a core which we call a \(k\)-tree core. Given a tree \(T\) and parameter \(k\), a \(k\)-tree core is a subtree \(T^{\pr