最大 1 平面图中的大匹配

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2024-10-24 DOI:10.1016/j.disc.2024.114288

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引用次数: 0

摘要

众所周知，如果 n≥14 ，则每个最大平面图的匹配大小至少为 n+83。在本文中，我们将研究最大 1-planar 图的类似匹配边界，即可以画出每条边最多有一个交叉点的图。特别是，我们证明了每个 3 连接的简单最大 1-planar 图都有一个大小至少为 2n+65 的匹配；如果图不需要是 3 连接的，则边界会减小到 3n+1410。当图形带有固定的 1-planar 图或不简单时，我们也给出了（较弱的）边界。我们的所有约束都很严格，因为满足限制条件的某些图没有更大的匹配。

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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Large matchings in maximal 1-planar graphs

It is well-known that every maximal planar graph has a matching of size at least

\frac{n + 8}{3}

n \geq 14

. In this paper, we investigate similar matching-bounds for maximal 1-planar graphs, i.e., graphs that can be drawn such that every edge has at most one crossing. In particular we show that every 3-connected simple-maximal 1-planar graph has a matching of size at least

\frac{2 n + 6}{5}

; the bound decreases to

\frac{3 n + 14}{10}

if the graph need not be 3-connected. We also give (weaker) bounds when the graph comes with a fixed 1-planar drawing or is not simple. All our bounds are tight in the sense that some graph that satisfies the restrictions has no bigger matching.

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来源期刊

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.