Exploring temporal graphs

10^th February 2026, 13:00 Ashton Lecture Theatre
Paul Bastide
University of Oxford

Abstract

A temporal graph G is a sequence of graphs G1, G2, ... , Gt on the same vertex set. In this talk, we are interested in the analogue of the Travelling Salesman Problem for temporal graphs. It is referred to in the literature as the Temporal Exploration Problem, and asks for the minimum length of an exploration of the graph, that is, a sequence of vertices such that at each time step t, one either stays at the same vertex or moves along a single edge of Gt.

One natural and still open case is when each graph Gt is connected and has bounded maximum degree. We present a short proof that any such graph admits an exploration in O(n^(3/2) log n^(1/2)) time steps. In fact, we deduce this result from a more general statement by introducing the notion of average temporal maximum degree. This more general statement improves the previous best bounds, under a unified approach, for several studied exploration problems.

This is based on joint work with Carla Groenland, Lukas Michel and Clément Rambaud.

Additional Materials

• https://arxiv.org/abs/2511.22604