7-连通极大1-平面图的匹配可扩展性

IF 0.5 4区数学 Q3 MATHEMATICS

Discussiones Mathematicae Graph Theory Pub Date : 2022-09-30 DOI:10.7151/dmgt.2470

Yuanqiu Huang, Licheng Zhang, Yuxi Wang

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引用次数: 2

摘要

如果图的每条边最多相交一次，那么它就是平面图。图和一平面图一起称为一平面。如果每个大小为k的匹配都可以扩展为完美匹配，则称图是k(≥1)可扩展的。已知单平面图的顶点连通性最多为7。本文刻画了7连通极大1平面图的k可拓性。我们证明了对于1≤k≤3，每一个偶阶的7连通极大1平面图都是k可扩展的。对于4≤k≤11，任何7连通极大1平面图都是不可k可拓的。当k≥12时，除非n = 2k，否则任何有n个顶点的7连通极大1平面图都是不可k可拓的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The Matching Extendability of 7-Connected Maximal 1-Plane Graphs

Abstract A graph is 1-planar if it can be drawn in the plane such that each edge is crossed at most once. A graph, together with a 1-planar drawing is called 1-plane. A graph is said to be k(≥1)-extendable if every matching of size k can be extended to a perfect matching. It is known that the vertex connectivity of a 1-plane graph is at most 7. In this paper, we characterize the k-extendability of 7-connected maximal 1-plane graphs. We show that every 7-connected maximal 1-plane graph with even order is k-extendable for 1 ≤ k ≤ 3. And any 7-connected maximal 1-plane graph is not k-extendable for 4 ≤ k ≤ 11. As for k ≥ 12, any 7-connected maximal 1-plane graph with n vertices is not k-extendable unless n = 2k.

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来源期刊

Discussiones Mathematicae Graph Theory MATHEMATICS-

CiteScore

2.20

自引率

0.00%

发文量

审稿时长

53 weeks

期刊介绍： The Discussiones Mathematicae Graph Theory publishes high-quality refereed original papers. Occasionally, very authoritative expository survey articles and notes of exceptional value can be published. The journal is mainly devoted to the following topics in Graph Theory: colourings, partitions (general colourings), hereditary properties, independence and domination, structures in graphs (sets, paths, cycles, etc.), local properties, products of graphs as well as graph algorithms related to these topics.