生成1-平面图的平面子图

IF 1 3区数学 Q2 MATHEMATICS

Journal of Graph Theory Pub Date : 2025-06-22 DOI:10.1002/jgt.23273

Kenta Noguchi, Katsuhiro Ota, Yusuke Suzuki

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引用次数: 0

摘要

在平面上绘制的图形，如果每条边最多与另一条边相交一次，则称为1-平面。本文证明了每一个四边连通的1-平面图都有一个连通的生成平面子图。我们还证明了存在无穷多个没有2连通生成平面子图的4连通1平面图。此外,我们考虑k和l的条件使得每一个k-连通1-平面图有一个-连通生成平面子图。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Spanning Plane Subgraphs of 1-Plane Graphs

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Spanning Plane Subgraphs of 1-Plane Graphs

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

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来源期刊

Journal of Graph Theory 数学-数学

CiteScore

1.60

自引率

22.20%

发文量

130

审稿时长

6-12 weeks

期刊介绍： The Journal of Graph Theory is devoted to a variety of topics in graph theory, such as structural results about graphs, graph algorithms with theoretical emphasis, and discrete optimization on graphs. The scope of the journal also includes related areas in combinatorics and the interaction of graph theory with other mathematical sciences. A subscription to the Journal of Graph Theory includes a subscription to the Journal of Combinatorial Designs .