The Complexity of Temporal Vertex Cover in Small-Degree Graphs

Temporal graphs naturally model whose underlying topology changes over time. Recently, the problems Vertex Cover (or TVC) and Sliding-Window Delta-TVC for time-windows of a fixed-length Delta) have been established as natural extensions classic problem on static with connections to areas such surveillance in sensor networks. In this paper we initiate systematic study complexity TVC sparse graphs. Our main result shows that every Delta geq 2, is NP-hard even when described by path or cycle. This resolves an open from literature surprising contrast between which provide polynomial-time algorithm same setting. To circumvent hardness, present number exact approximation algorithms temporal topologies are given path, bounded vertex degree time step, admit small-sized cover.