A note on distance-hereditary graphs whose complement is also distance-hereditary

[2504.12857] A note on distance-hereditary graphs whose complement is also distance-hereditary Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Combinatorics arXiv:2504.12857 (math) [Submitted on 17 Apr 2025 ( v1 ), last revised 10 Apr 2026 (this version, v2)] Title: A note on distance-hereditary graphs whose complement is also distance-hereditary Authors: Hugo Jacob View a PDF of the paper titled A note on distance-hereditary graphs whose complement is also distance-hereditary, by Hugo Jacob View PDF HTML (experimental) Abstract: Distance-hereditary graphs are known to be the graphs that are totally decomposable for the split decomposition. We characterise distance-hereditary graphs whose complement is also distance-hereditary by their split decomposition and by their modular decomposition. Comments: 6 pages, 4 figures Subjects: Combinatorics (math.CO) ; Discrete Mathematics (cs.DM) Cite as: arXiv:2504.12857 [math.CO] (or arXiv:2504.12857v2 [math.CO] for this version) https://doi.org/10.48550/arXiv.2504.12857 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Discrete Applied Mathematics, Volume 390, 15 September 2026, Pages 57-61 Related DOI : https://doi.org/10.1016/j.dam.2026.04.004 Focus to learn more DOI(s) linking to related resources Submission history From: Hugo Jacob [ view email ] [v1] Thu, 17 Apr 2025 11:29:10 UTC (30 KB) [v2] Fri, 10 Apr 2026 11:27:51 UTC (31 KB) Full-text links: Access Paper: View a PDF of the paper titled A note on distance-hereditary graphs whose complement is also distance-hereditary, by Hugo Jacob View PDF HTML (experimental) TeX Source view license Current browse context: math.CO < prev | next > new | recent | 2025-04 Change to browse by: cs cs.DM 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

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