Temporal Exploration of Random Spanning Tree Models

The Temporal Graph Exploration problem (TEXP) takes as input a temporal graph, i.e., a sequence of graphs \((G_i)_{i\in\mathbb N}\) on the same vertex set, and asks for a walk of shortest length visiting all vertices, where the \(i\)-th step uses an edge from \(G_i\) or stays put. If each such \(G_i\) is connected, then an exploration of length \(n^2\) exists, and this is known to be the best possible up to a constant. More fine-grained lower and upper bounds have been obtained for restricted temporal graph classes, however, for several fundamental classes, a large gap persists between known bounds, and it remains unclear which properties of a temporal graph make it inherently difficult to explore.