Set recognition of decomposable graphs and steps towards their reconstruction

IF 0.4 4区数学 Q4 MATHEMATICS

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2022-01-03 DOI:10.1007/s12188-021-00252-0

Bernd S. W. Schröder

引用次数: 2

Abstract

It is proved that decomposable graphs are set recognizable and that the index graph of the canonical decomposition as well as the graphs induced on the maximal autonomous sets of vertices are set reconstructible. From these results, we obtain set reconstructibility for many decomposable graphs as well as a concise description of the decomposable graphs for which set reconstruction remains an open problem.

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设置可分解图的识别和重建步骤

证明了可分解图是集可识别的，正则分解的索引图和在顶点的最大自治集上导出的图是集可重构的。从这些结果中，我们得到了许多可分解图的集合可重构性，以及集合重构仍然是一个开放问题的可分解图的简明描述。

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

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 数学-数学

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The first issue of the "Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg" was published in the year 1921. This international mathematical journal has since then provided a forum for significant research contributions. The journal covers all central areas of pure mathematics, such as algebra, complex analysis and geometry, differential geometry and global analysis, graph theory and discrete mathematics, Lie theory, number theory, and algebraic topology.