Abstract
AbstractIn this paper, we prove several inapproximability results on the P 3-convexity and the geodetic convexity on graphs. We prove that determining the P 3-hull number and the geodetic hull number are APX-hard problems. We prove that the Carathéodory number, the Radon number and the convexity number of both convexities are O(n 1 − ε)-inapproximable in polynomial time for every ε > 0, unless P=NP. We also prove that the interval numbers of both convexities are W[2]-hard and O(logn)-inapproximable in polynomial time, unless P=NP. Moreover, these results hold for bipartite graphs in the P 3-convexity.Keywords P 3-convexitygeodetic convexityAPX-hardnessinapproximability resultshull numberCarathéodory numberRadon numberconvexity numberinterval number
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