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Journal of Graph Theory
Article . 2025 . Peer-reviewed
License: CC BY NC ND
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arXiv.org e-Print Archive
Preprint . 2024
Data sources: arXiv.org e-Print Archive
https://dx.doi.org/10.48550/ar...
Article . 2024
License: arXiv Non-Exclusive Distribution
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Spanning Plane Subgraphs of 1‐Plane Graphs

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 22 Jun 2025Embargo end date: 01 Jan 2024 English Publisher:WileyJournal:Journal of Graph Theory, volume 110, pages 290-297 (issn: 0364-9024, eissn: 1097-0118, Copyright policy )
Authors: Kenta Noguchi; Katsuhiro Ota; Yusuke Suzuki;

doi: 10.1002/jgt.23273 , 10.48550/arxiv.2404.05394

arXiv: http://arxiv.org/abs/2404.05394

Spanning Plane Subgraphs of 1‐Plane Graphs

Abstract

ABSTRACTA graph drawn on the plane is called 1‐plane if each edge is crossed at most once by another edge. In this paper, we show that every 4‐edge‐connected 1‐plane graph has a connected spanning plane subgraph. We also show that there exist infinitely many 4‐connected 1‐plane graphs that have no 2‐connected spanning plane subgraphs. Moreover, we consider the condition of and such that every ‐connected 1‐plane graph has an ‐connected spanning plane subgraph.

Related Organizations
Keywords

05C10, 05C70, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO)

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
Green
hybrid