On the minimum size of maximal IC-plane graphs

A graph is IC-planar if it admits a drawing with at most one crossing per edge so that each vertex is incident to at most one crossing edge, and an IC-plane graph means such a drawing of an IC-planar graph. We show that any maximal IC-plane graph with $ n $ vertices has at least $ 2n-2 $ edges.

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Publication Details

Journal
AIMS Mathematics
Published
2025-01-01
DOI
https://doi.org/10.3934/math.2025643
Primary Topic
Advanced Graph Theory Research
Type
article
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article

On the minimum size of maximal IC-plane graphs

Rui Xu
AIMS Mathematics
Advanced Graph Theory Research
article

On the minimum size of maximal IC-plane graphs

Rui Xu
article en

Abstract

A graph is IC-planar if it admits a drawing with at most one crossing per edge so that each vertex is incident to at most one crossing edge, and an IC-plane graph means such a drawing of an IC-planar graph. We show that any maximal IC-plane graph with $ n $ vertices has at least $ 2n-2 $ edges.

AIMS MathematicsVol. 10(6)
Hunan Normal University (CN)
Openalex Percentile: Top 84%
Advanced Graph Theory Research
DOIOpen Access PDFOpenAlex
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On the minimum size of maximal IC-plane graphs — Rui Xu · AIMS Mathematics (2025) | TGRS Research Map | TGRS