Set recognition of decomposable graphs and steps towards their reconstruction

Set recognition of decomposable graphs and steps towards their reconstruction

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 we...

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Veröffentlicht in:Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 2022, Vol.92 (1), p.1-25
1. Verfasser: Schröder, Bernd S. W.
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Apexes
Decomposition
Differential Geometry
Geometry
Graphs
Mathematics
Mathematics and Statistics
Number Theory
Reconstruction
Topology
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Zusammenfassung: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.
ISSN:0025-5858
1865-8784
DOI:10.1007/s12188-021-00252-0