Edge exploration of temporal graphs

Bumpus, B. M. and Meeks, K. (2021) Edge exploration of temporal graphs. In: 32nd International Workshop on Combinatorial Algorithms (IWOCA 2021), 05-07 Jul 2021, pp. 107-121. ISBN 9783030799861 (doi: 10.1007/978-3-030-79987-8_8)

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Abstract

We introduce a natural temporal analogue of Eulerian circuits and prove that, in contrast with 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:Conference Proceedings
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Bumpus, Benjamin and Meeks, Dr Kitty
Authors: Bumpus, B. M., and Meeks, K.
College/School:College of Science and Engineering > School of Computing Science
ISSN:0302-9743
ISBN:9783030799861
Published Online:30 June 2021
Copyright Holders:Copyright © 2021 Springer Nature Switzerland AG
First Published:First published in Lecture Notes in Computer Science 12757: 107-121
Publisher Policy:Reproduced in accordance with the publisher copyright policy
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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
305944Multilayer Algorithmics to Leverage Graph StructureKitty MeeksEngineering and Physical Sciences Research Council (EPSRC)EP/T004878/1M&S - Statistics
172865EPSRC DTP 16/17 and 17/18Tania GalabovaEngineering and Physical Sciences Research Council (EPSRC)EP/N509668/1Research and Innovation Services