An optimal construction for complete graph embeddings with duals of low connectivity

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-06-20 DOI:10.1016/j.disc.2025.114628

Timothy Sun

引用次数: 0

Abstract

We describe a construction for embeddings of complete graphs where the dual has a cutvertex and the genus of the embedding is close to the minimum genus of the primal graph. When the number of vertices is congruent to 2 or 5 modulo 12, we further guarantee that the dual is simple and that the genus of the resulting embeddings matches a lower bound of Brinkmann, Noguchi, and Van den Camp, showing that their lower bound is tight infinitely often.

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具有低连通性对偶的完全图嵌入的最优构造

我们描述了对偶具有切顶点且嵌入的格值接近原始图的最小格值的完全图的嵌入的一种构造。当顶点数等于2或5模12时，我们进一步保证对偶是简单的，并且所得到的嵌入的属匹配Brinkmann、Noguchi和Van den Camp的下界，表明它们的下界常常是紧的。

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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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.