BIROn - Birkbeck Institutional Research Online

Graphs without proper subgraphs of minimum degree 3 and short cycles

Narins, L. and Pokrovskiy, Alexey and Szabó, T. (2016) Graphs without proper subgraphs of minimum degree 3 and short cycles. Combinatorica 37 (3), pp. 495-519. ISSN 0209-9683.

[img]
Preview
Text
1408.5289.pdf - Author's Accepted Manuscript

Download (252kB) | Preview

Abstract

We study graphs on n vertices which have 2n−2 edges and no proper induced subgraphs of minimum degree 3. Erdős, Faudree, Gyárfás, and Schelp conjectured that such graphs always have cycles of lengths 3,4,5,…,C(n) for some function C(n) tending to infinity. We disprove this conjecture, resolve a related problem about leaf-to-leaf path lengths in trees, and characterize graphs with n vertices and 2n−2 edges, containing no proper subgraph of minimum degree 3.

Metadata

Item Type: Article
Additional Information: The final publication is available at Springer via the link above.
School: Birkbeck Faculties and Schools > Faculty of Business and Law > Birkbeck Business School
Depositing User: Alexey Pokrovskiy
Date Deposited: 21 Jan 2019 11:20
Last Modified: 14 Jul 2025 17:09
URI: https://eprints.bbk.ac.uk/id/eprint/25892

Statistics

6 month trend
361Downloads
6 month trend
171Hits

Additional statistics are available via IRStats2.

Archive Staff Only (login required)

Edit/View Item
Edit/View Item