Sharp Bounds for the Oriented Diameters of Interval Graphs and 2-Connected Proper Interval Graphs
نویسندگان
چکیده
The diameter diam(H) of a (directed) graph H is the maximum value computed over the lengths of all shortest (directed) paths in H . Given a bridgeless connected graph G, the oriented diameter OD(G) is given by OD(G) = min{diam(H) : H is an orientation of G}. In this paper, we show that OD(G) ≤ 2diam(G) +1 for every connected bridgeless interval graph G. Further, for every 2-connected proper interval graph G, we show OD(G) ≤ 4diam(G) + 1 if diam(G) ≤ 3 and OD(G) ≤ 4diam(G) , otherwise. All the bounds are sharp and improve earlier estimations obtained by Fomin et al.
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