𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Tree-width and circumference of graphs

✍ Scribed by Etienne Birmele

Publisher
John Wiley and Sons
Year
2003
Tongue
English
Weight
37 KB
Volume
43
Category
Article
ISSN
0364-9024

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

We prove that every graph of circumference k has tree‐width at most kβ€‰βˆ’β€‰1 and that this bound is best possible. Β© 2003 Wiley Periodicals, Inc. J Graph Theory 43: 24–25, 2003

πŸ“œ SIMILAR VOLUMES

Efficient Parallel Algorithms for Graphs
Efficient Parallel Algorithms for Graphs of Bounded Tree-Width
✍ Jens Lagergren πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 236 KB

We present an efficient parallel algorithm for the tree-decomposition problem Ε½ 3 . Ε½. for fixed width w. The algorithm runs in time O O log n and uses O O n processors on an ARBITRARY CRCW PRAM. The sequential complexity of our tree-decom-Ε½ 2 . position algorithm is O O n log n . The tree-decomposi

Optimal Parametric Search on Graphs of B
Optimal Parametric Search on Graphs of Bounded Tree-Width
✍ David FernΓ‘ndez-Baca; Giora Slutzki πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 339 KB

We give linear-time algorithms for a class of parametric search problems on weighted graphs of bounded tree-width. We also discuss the implications of our results to approximate parametric search on planar graphs.

Ka,k Minors in Graphs of Bounded Tree-Wi
Ka,k Minors in Graphs of Bounded Tree-Width
✍ Thomas BΓΆhme; John Maharry; Bojan Mohar πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 175 KB

It is shown that for any positive integers k and w there exists a constant N ¼ N ðk; wÞ such that every 7-connected graph of tree-width less than w and of order at least N contains K 3;k as a minor. Similar result is proved for K a;k minors where a is an arbitrary fixed integer and the required conn

Circumference of a regular graph
Circumference of a regular graph
✍ Min Aung πŸ“‚ Article πŸ“… 1989 πŸ› John Wiley and Sons 🌐 English βš– 251 KB
The plane-width of graphs
The plane-width of graphs
✍ Marcin KamiΕ„ski; Paul Medvedev; Martin Milanič πŸ“‚ Article πŸ“… 2011 πŸ› John Wiley and Sons 🌐 English βš– 192 KB

Map the vertices of a graph to (not necessarily distinct) points of the plane so that two adjacent vertices are mapped at least unit distance apart. The plane-width of a graph is the minimum diameter of the image of its vertex set over all such mappings. We establish a relation between the plane-wid