S. Brandt
Global connectivity and expansion : long cycles and factors in f-connected graphs
Brandt, S.; Broersma, H.J.; Diestel, R.; Kriesell, M.
Authors
H.J. Broersma
R. Diestel
M. Kriesell
Abstract
Given a function f : N → R, call an n-vertex graph f-connected if separating off k vertices requires the deletion of at least f(k) vertices whenever k ≤ (n−f(k))/2. This is a common generalization of vertex connectivity (when f is constant) and expansion (when f is linear). We show that an f-connected graph contains a cycle of length linear in n if f is any linear function, contains a 1-factor and a 2-factor if f(k) ≥ 2k + 1, and contains a Hamilton cycle if f(k) ≥ 2(k + 1)2. We conjecture that linear growth of f suffices to imply hamiltonicity.
Citation
Brandt, S., Broersma, H., Diestel, R., & Kriesell, M. (2006). Global connectivity and expansion : long cycles and factors in f-connected graphs. Combinatorica, 26(1), 17-36. https://doi.org/10.1007/s00493-006-0002-5
Journal Article Type | Article |
---|---|
Publication Date | 2006 |
Deposit Date | Jan 12, 2007 |
Journal | Combinatorica |
Print ISSN | 0209-9683 |
Electronic ISSN | 1439-6912 |
Publisher | Springer |
Peer Reviewed | Peer Reviewed |
Volume | 26 |
Issue | 1 |
Pages | 17-36 |
DOI | https://doi.org/10.1007/s00493-006-0002-5 |
Keywords | Global connectivity, Factor, Long cycle, Hamiltonian cycle. |
You might also like
Fully decomposable split graphs
(2009)
Conference Proceeding
On hamiltonicity of P3-dominated graphs
(2009)
Journal Article
Upper bounds and algorithms for parallel knock-out numbers
(2009)
Journal Article
Complexity of conditional colorability of graphs
(2009)
Journal Article
Planar graph coloring avoiding monochromatic subgraphs : trees and paths make it difficult
(2006)
Journal Article
Downloadable Citations
About Durham Research Online (DRO)
Administrator e-mail: dro.admin@durham.ac.uk
This application uses the following open-source libraries:
SheetJS Community Edition
Apache License Version 2.0 (http://www.apache.org/licenses/)
PDF.js
Apache License Version 2.0 (http://www.apache.org/licenses/)
Font Awesome
SIL OFL 1.1 (http://scripts.sil.org/OFL)
MIT License (http://opensource.org/licenses/mit-license.html)
CC BY 3.0 ( http://creativecommons.org/licenses/by/3.0/)
Powered by Worktribe © 2024
Advanced Search