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Alecu, Bogdan, Atminas, Aistis and Lozin, Vadim V. (2021) Graph functionality. Journal of Combinatorial Theory, Series B, 147 . pp. 139-158. doi:10.1016/j.jctb.2020.11.002

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Official URL: http://dx.doi.org/10.1016/j.jctb.2020.11.002

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Abstract

In the present paper, we introduce the notion of graph functionality, which generalises simultaneously several other graph parameters, such as degeneracy or clique-width, in the sense that bounded degeneracy or bounded clique-width imply bounded functionality. Moreover, we show that this generalisation is proper by revealing classes of graphs of unbounded degeneracy and clique-width, where functionality is bounded by a constant. We also prove that bounded functionality implies bounded VC-dimension, i.e., graphs of bounded VC-dimension extend graphs of bounded functionality, and this extension is also proper.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software
Divisions: Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH): Computer algorithms, Graph theory, Algorithms, Computer science -- Mathematics, Computer graphics
Journal or Publication Title: Journal of Combinatorial Theory, Series B
Publisher: Academic Press
ISSN: 0095-8956
Official Date: March 2021
Dates:
DateEvent
March 2021Published
17 November 2020Available
6 November 2020Accepted
Date of first compliant deposit: 26 November 2020
Volume: 147
Page Range: pp. 139-158
DOI: 10.1016/j.jctb.2020.11.002
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Description:

Some results presented in this paper appeared in the extended abstract [1] published in the proceedings of the 45th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2019.

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