20.500.12556/RUL-139072 The general position achievement game played on graphs A general position set of a graph G is a set of vertices S in G such that no three vertices from S lie on a common shortest path. In this paper we introduce and study the general position achievement game. The game is played on a graph G by players A and B who alternatively pick vertices of G. A selection of a vertex is legal if has not been selected before and the set of vertices selected so far forms a general position set of G. The player who selects the last vertex wins the game. Playable vertices at each step of the game are described, and sufficient conditions for each of the players to win is given. The game is studied on Cartesian and lexicographic products. Among other results it is proved that A wins the game on K$_n$ □ K$_m$ if and only if both n and m are odd, and that B wins the game on G ∘ K$_n$ if and only if either B wins on G or n is even. general position set achievement game Cartesian product of graphs lexicographic product of graphs množica v splošni legi igra doseganja kartezični produkt grafov leksikografski produkt grafov true false true Angleški jezik Slovenski jezik Članek v reviji 2022-08-30 08:57:38 2022-08-30 08:57:42 2022-09-15 04:17:46 0000-00-00 00:00:00 2022 0 0 Str. 109-116 Vol. 317 Aug. 2022 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.17 0166-218X 10.1016/j.dam.2022.04.019 108461571 1-s2.0-S0166218X2200141X-main.pdf 1-s2.0-S0166218X2200141X-main.pdf 1 F4C7D62A0AA4738DDB0C2ACAEAE50F36 75e0b940a2639277c4165e3ef6dab5d9d9d96254e4206aee2dd14bde50dfbbab f3ada189-2831-11ed-92af-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=159604 https://www.sciencedirect.com/science/article/pii/S0166218X2200141X 1 027c5358-2831-11ed-92af-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=159597 Fakulteta za matematiko in fiziko 0 0 0