Spanning plane subgraphs of $1$-plane graphs

Kenta Noguchi; Katsuhiro Ota; Yusuke Suzuki

Spanning plane subgraphs of $1$-plane graphs

Combinatorics 2024-04-09 v1

Authors: Kenta Noguchi , Katsuhiro Ota , Yusuke Suzuki

Abstract

A 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 $4$ -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 $k$ and $l$ such that every $k$ -connected $1$ -plane graph has an $l$ -connected spanning plane subgraph.

Keywords

graph theory graph connectivity graph pebbling

Cite

@article{arxiv.2404.05394,
  title  = {Spanning plane subgraphs of $1$-plane graphs},
  author = {Kenta Noguchi and Katsuhiro Ota and Yusuke Suzuki},
  journal= {arXiv preprint arXiv:2404.05394},
  year   = {2024}
}

Comments

10 pages, 5 figures

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