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Abstract: The edge geodesic cover problem of a graph G is to find a smallest number of geodesics that cover the edge set of G. The edge k-general position problem is introduced as the problem to find a largest set S of edges of G such that at most k-1 edges of S lie on a common geodesic. We show that these are dual min-max problems and connect them to an edge geodesic partition problem. Using these connections, exact values of the edge k-general position number is determined for different values of k and for various networks including torus networks, hypercubes, and Benes networks.
Keywords: general position set, edge geodesic cover problem, edge k-general position problem, torus network, hypercube, Benes network
Published in RUP: 03.11.2025; Views: 256; Downloads: 1
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