Algorithm for Online 3-Path Vertex Cover

A vertex set C of a graph G = (V, E) is a 3-path vertex cover if every path on 3 vertices has at least one vertex in C. This paper studies the online version of the minimum 3-path vertex cover problem, in which vertices are revealed one by one, and one has to determine whether the newly revealed vertex should be chosen into the solution without knowing future information. We show that a natural algorithm has competitive ratio at most Δ, where Δ is the maximum degree of the graph. An example is given showing that the ratio is tight.