Combinatorial rigidity and flexibility of simplicial 2-complexes with few vertices

Authors

Serge A. Lawrence, Institute of Service Technologies, Russian State University of Tourism and Service, Podolsk 142116, Russian FederationFollow
Abdulkarim M. Magomedov, Dagestan Federal Research Center, Dagestan 367032, Russian FederationFollow
Olga I. Chelyapina, Institute of Service Technologies, Russian State University of Tourism and Service, Podolsk 142116, Russian FederationFollow
Valentina M. Rudenko, Institute of Service Technologies, Russian State University of Tourism and Service, Podolsk 142116, Russian FederationFollow

Publication Date

April 2025

Abstract

We study the problem of reconstruction of a simplicial 2-complex from its 1- skeleton together with the prescribed quantities of 2-simplices at each 1-simplex, under the restriction that these quantities are bounded above by 2. It is a known fact that a 2-complex is uniquely reconstructible, or “combinatorially rigid”, if it has 5 or fewer vertices. In this paper “combinatorially flexible” 2-complexes (that is, non-uniquely reconstructible from their 1-skeletons) with 6 vertices are characterized in terms of necessary 2-subcomplexes.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.

Recommended Citation

Lawrence, Serge A.; Magomedov, Abdulkarim M.; Chelyapina, Olga I.; and Rudenko, Valentina M. (2025) "Combinatorial rigidity and flexibility of simplicial 2-complexes with few vertices," Theory and Applications of Graphs: Vol. 12: Iss. 1, Article 2.
DOI: 10.20429/tag.2025.120102
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol12/iss1/2