Edge exploration of temporal graphs

Bumpus, B. M. and Meeks, K. (2023) Edge exploration of temporal graphs. Algorithmica, 85(3), pp. 688-716. (doi: 10.1007/s00453-022-01018-7)

Abstract

We introduce a natural temporal analogue of Eulerian circuits and prove that, in contrast to the static case, it is NP-hard to determine whether a given temporal graph is temporally Eulerian even if strong restrictions are placed on the structure of the underlying graph and each edge is active at only three times. However, we do obtain an FPT-algorithm with respect to a new parameter called interval-membership-width which restricts the times assigned to different edges; we believe that this parameter will be of independent interest for other temporal graph problems. Our techniques also allow us to resolve two open questions of Akrida, Mertzios and Spirakis [CIAC 2019] concerning a related problem of exploring temporal stars.

• Item Type: Articles
• Additional Information: The first author was supported by an EPSRC doctoral training account and also received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 803421, ReduceSearch). The second author was supported by a Royal Society of Edinburgh Personal Research Fellowship, funded by the Scottish Government, and EPSRC grant EP/T004878/1.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Meeks, Dr Kitty and Bumpus, Benjamin
• Authors: Bumpus, B. M., and Meeks, K.
• College/School: College of Science and Engineering > School of Computing Science
• Journal Name: Algorithmica
• Publisher: Springer
• ISSN: 0178-4617
• ISSN (Online): 1432-0541
• Published Online: 22 August 2022
• Copyright Holders: Copyright © 2022 The Authors
• First Published: First published in Algorithmica 85(3) 688-716
• Publisher Policy: Reproduced under a Creative Commons License

Project Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
305944		Multilayer Algorithmics to Leverage Graph Structure	Kitty Meeks	Engineering and Physical Sciences Research Council (EPSRC)	EP/T004878/1	M&S - Statistics
172865		EPSRC DTP 16/17 and 17/18	Mary Beth Kneafsey	Engineering and Physical Sciences Research Council (EPSRC)	EP/N509668/1	Research and Innovation Services