Alecu, B. orcid.org/0000-0002-5515-9145, Alekseev, V.E., Atminas, A. et al. (2 more authors) (2023) Graph parameters, implicit representations and factorial properties. Discrete Mathematics, 346 (10). 113573. ISSN 0012-365X
Abstract
How to efficiently represent a graph in computer memory is a fundamental data structuring question. In the present paper, we address this question from a combinatorial point of view. A representation of an n-vertex graph G is called implicit if it assigns to each vertex of G a binary code of length O(logn) so that the adjacency of two vertices is a function of their codes. A necessary condition for a hereditary class X of graphs to admit an implicit representation is that X has at most factorial speed of growth. This condition, however, is not sufficient, as was recently shown in [19]. Several sufficient conditions for the existence of implicit representations deal with boundedness of some parameters, such as degeneracy or clique-width. In the present paper, we analyze more graph parameters and prove a number of new results related to implicit representation and factorial properties.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). |
Keywords: | Graph parameter; Implicit representation; Hereditary class; Factorial property; Combinatorial Algorithms; IWOCA 2022 |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) > Algorithms & Complexity |
Depositing User: | Symplectic Publications |
Date Deposited: | 25 Apr 2024 11:26 |
Last Modified: | 25 Apr 2024 11:26 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.disc.2023.113573 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:211809 |