20.500.12556/RUP-22059 Generalization of edge general position problem Posplošitev povezavnega splošnega položajnega problema 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. general position set edge geodesic cover problem edge k-general position problem torus network hypercube Benes network splošna položajna množica povezavni geodetski problem pokritja povezavnik-splošni položajni problem torusna mreža hiperkocka Benesova mreža true false true Založba Univerze na Primorskem Angleški jezik Slovenski jezik Članek v reviji 2025-11-03 10:01:32 2025-11-03 10:01:33 2025-11-04 03:08:24 0000-00-00 00:00:00 2025 0 0 12 str. no. 1, [article no.] P1.02 Vol. 8 2025 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2025-02-20 51 2590-9770 https://doi.org/10.26493/2590-9770.1745.5f4 ADAM_Manuel,Prabha,Klavzar_2025.pdf ADAM_Manuel,Prabha,Klavzar_2025.pdf 1 386F8DDD74322661E60021DF3F37B293 8a2bf6566ff72b3efd9272582f03bb4023a390bc54ff18370f8731456634002f 7bbfbc57-b894-11f0-8f0b-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=32004 Založba Univerze na Primorskem 0 0 0