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Exploration of k-Edge-Deficient Temporal Graphs

Erlebach, Thomas; Spooner, Jakob T.

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Authors

Jakob T. Spooner



Abstract

A temporal graph with lifetime L is a sequence of L graphs G1, . . . , GL, called layers, all of which have the same vertex set V but can have different edge sets. The underlying graph is the graph with vertex set V that contains all the edges that appear in at least one layer. The temporal graph is always-connected if each layer is a connected graph, and it is k-edge-decient if each layer contains all except at most k edges of the underlying graph. For a given start vertex s, a temporal exploration is a temporal walk that starts at s, traverses at most one edge in each layer, and visits all vertices of the temporal graph. We show that always- connected, k-edge-decient temporal graphs with sucient lifetime can always be explored in O(kn log n) time steps. We also construct always-connected, k-edge- decient temporal graphs for which any exploration requires (n log k) time steps. For always-connected, 1-edge-decient temporal graphs, we show that O(n) time steps suce for temporal exploration.

Citation

Erlebach, T., & Spooner, J. T. (2022). Exploration of k-Edge-Deficient Temporal Graphs. Acta Informatica, 59(4), 387-407. https://doi.org/10.1007/s00236-022-00421-5

Journal Article Type Article
Acceptance Date Mar 28, 2022
Online Publication Date Aug 27, 2022
Publication Date 2022-08
Deposit Date Apr 10, 2022
Publicly Available Date Mar 28, 2024
Journal Acta Informatica
Print ISSN 0001-5903
Electronic ISSN 1432-0525
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 59
Issue 4
Pages 387-407
DOI https://doi.org/10.1007/s00236-022-00421-5

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http://creativecommons.org/licenses/by/4.0/

Copyright Statement
This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.





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