2-Connected spanning subgraphs of circuit graphs

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2024-09-03 DOI:10.1016/j.disc.2024.114228

Atsuhiro Nakamoto , Kenta Ozeki , Daiki Takahashi

引用次数: 0

Abstract

Kaneko et al. [12] proved that every 3-connected planar graph G has a 2-connected spanning subgraph K such that $| E (K) | \leq \frac{4}{3} (| V (G) | - 1)$ , and they also conjectured that the constant of the estimation can be improved to $\frac{4}{3} (| V (G) | - 2)$ when $| V (G) | \geq 8$ . To prove the result, they showed the statement for a circuit graph, which is obtained from a 3-connected planar graph by deleting one vertex, and the theorem is best possible for circuit graphs. In this paper, we give a characterization of a circuit graph G each of whose 2-connected spanning subgraph K requires $| E (K) | \geq \frac{4}{3} (| V (G) | - 1)$ and then we improve the bound for the 3-connected planar case.

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2 电路图的连接跨度子图

Kaneko 等人[12]证明了每个 3 连平面图 G 都有一个 2 连跨子图 K，使得|E(K)|≤43(|V(G)|-1)，他们还猜想当|V(G)|≥8 时，估计常数可以提高到 43(|V(G)|-2)。为了证明这一结果，他们展示了电路图的声明，电路图是通过删除一个顶点从 3 连接的平面图中得到的，该定理对于电路图是最可行的。在本文中，我们给出了电路图 G 的特征，每个电路图 G 的 2 连跨子图 K 都要求 |E(K)|≥43(|V(G)|-1) ，然后我们改进了 3 连平面图的约束。

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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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.