[2212.02079] Restriction on minimum degree in the contractible sets problem Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Combinatorics arXiv:2212.02079 (math) [Submitted on 5 Dec 2022 ( v1 ), last revised 30 Apr 2026 (this version, v2)] Title: Restriction on minimum degree in the contractible sets problem Authors: Nikolai Karol View a PDF of the paper titled Restriction on minimum degree in the contractible sets problem, by Nikolai Karol View PDF HTML (experimental) Abstract: Let $G$ be a $3$-connected graph. A set $W \subset V(G)$ is called contractible if $G(W)$ is a connected graph and $G - W$ is a $2$-connected graph. In 1994, McCuaig and Ota conjectured that for any $k \in \mathbb{N}$ there exists $n \in \mathbb{N}$ such that any 3-connected graph $G$ with $v(G) \geqslant n$ has a $k$-vertex contractible set. It is proved that this holds if $k \geqslant 5$ and $\delta(G) \geqslant \left[ \frac{2k + 1}{3} \right] + 2$. Subjects: Combinatorics (math.CO) MSC classes: 05C40 Cite as: arXiv:2212.02079 [math.CO] (or arXiv:2212.02079v2 [math.CO] for this version) https://doi.org/10.48550/arXiv.2212.02079 Focus to learn more arXiv-issued DOI via DataCite Journal reference: J. Math. Sci., 297, 410-416, 2026 Submission history From: Nikolai Karol [ view email ] [v1] Mon, 5 Dec 2022 07:48:40 UTC (24 KB) [v2] Thu, 30 Apr 2026 03:55:19 UTC (22 KB) Full-text links: Access Paper: View a PDF of the paper titled Restriction on minimum degree in the contractible sets problem, by Nikolai Karol View PDF HTML (experimental) TeX Source view license Current browse context: math.CO < prev | next > new | recent | 2022-12 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from