The general position achievement game played on graphs

Klavžar, Sandi (avtor), Neethu, P.K. (avtor), Ullas Chandran, S.V. (avtor)

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.

• Jezik: Angleški jezik
• Ključne besede: general position set, achievement game, Cartesian product of graphs, lexicographic product of graphs
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Leto izida: 2022
• Št. strani: Str. 109-116
• Številčenje: Vol. 317
• PID: 20.500.12556/RUL-139072
• UDK: 519.17
• ISSN pri članku: 0166-218X
• DOI: 10.1016/j.dam.2022.04.019
• COBISS.SI-ID: 108461571
• Datum objave v RUL: 30.08.2022

KLAVŽAR, Sandi, NEETHU, P.K. in ULLAS CHANDRAN, S.V., 2022, The general position achievement game played on graphs. Discrete applied mathematics [na spletu]. 2022. Vol. 317, p. 109–116. [Dostopano 26 april 2025]. DOI 10.1016/j.dam.2022.04.019. Pridobljeno s: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=slv&id=139072

Gradivo je del revije

• Naslov: Discrete applied mathematics
• Skrajšan naslov: Discrete appl. math.
• Založnik: Elsevier
• ISSN: 0166-218X
• COBISS.SI-ID: 25342464

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: množica v splošni legi, igra doseganja, kartezični produkt grafov, leksikografski produkt grafov