@inproceedings{32ecb8248bcd4a3591ec5f6a0f2d1489,
title = "Faster exploration of some temporal graphs",
abstract = "A temporal graph G = (G1, G2,..., GT ) is a graph represented by a sequence of T graphs over a common set of vertices, such that at the ith time step only the edge set Ei is active. The temporal graph exploration problem asks for a shortest temporal walk on some temporal graph visiting every vertex. We show that temporal graphs with n vertices can be explored in O(kn1.5 log n) days if the underlying graph has treewidth k and in O(n1.75 log n) days if the underlying graph is planar. Furthermore, we show that any temporal graph whose underlying graph is a cycle with k chords can be explored in at most 6kn days. Finally, we demonstrate that there are temporal realisations of sub cubic planar graphs that cannot be explored faster than in Ω(n log n) days. All these improve best known results in the literature.",
keywords = "Graph Exploration, Temporal Graphs",
author = "Duncan Adamson and Gusev, {Vladimir V.} and Dmitriy Malyshev and Viktor Zamaraev",
note = "Funding Adamson, Duncan: Funded by the Leverhulme trust. Gusev, Vladimir V.: funded by the Leverhulme trust. Malyshev, Dmitriy: The work of Dmitriy Malyshev was conducted within the framework of the Basic Research Program at the National Research University Higher School of Economics (HSE).; 1st Symposium on Algorithmic Foundations of Dynamic Networks, SAND 2022 ; Conference date: 28-03-2022 Through 30-03-2022",
year = "2022",
month = apr,
day = "29",
doi = "10.4230/LIPIcs.SAND.2022.5",
language = "English",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
editor = "James Aspnes and Othon Michail",
booktitle = "1st Symposium on Algorithmic Foundations of Dynamic Networks, SAND 2022",
}