Deploying robots with two sensors in K_{1, 6}-free graphs

Let G be a graph of minimum degree at least 2 with no induced subgraph isomorphic to K_{1, 6}. We prove that if G is not isomorphic to one of eight exceptional graphs, then it is possible to assign two-element subsets of {1,2,3,4,5} to the vertices of G in such a way that for every i∈{1,2,3,4,5} and every vertex v∈V(G) the label i is assigned to v or one of its neighbors. It follows that G has fractional domatic number at least 5/2. This is motivated by a problem in robotics and generalizes a result of Fujita, Yamashita, and Kameda who proved that the same conclusion holds for all 3-regular graphs.