The independence coloring game on graphs

Brešar, Boštjan (avtor), Mesarič Štesl, Daša (avtor)

We propose a new coloring game on a graph, called the independence coloring game, which is played by two players with opposite goals. The result of the game is a proper coloring of vertices of a graph G, and Alice’s goal is that as few colors as possible are used during the game, while Bob wants to maximize the number of colors. The game consists of rounds, and in round i, where i = 1, 2, , . . ., the players are taking turns in selecting a previously unselected vertex of G and giving it color i (hence, in each round the selected vertices form an independent set). The game ends when all vertices of G are selected (and thus colored), and the total number of rounds during the game when both players are playing optimally with respect to their goals, is called the independence game chromatic number, χ$_{ig}$(G), of G. In fact, four different versions of the independence game chromatic number are considered, which depend on who starts a game and who starts next rounds. We prove that the new invariants lie between the chromatic number of a graph and the maximum degree plus 1, and characterize the graphs in which each of the four versions of the game invariant equals 2. We compare the versions of the independence game chromatic number among themselves and with the classical game chromatic number. In addition, we prove that the independence game chromatic number of a tree can be arbitrarily large.

• Jezik: Angleški jezik
• Ključne besede: graph, coloring, coloring game, competition-independence game, game chromatic number, tree
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FRI - Fakulteta za računalništvo in informatiko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Leto izida: 2022
• Št. strani: Str. 1413-1434
• Številčenje: Vol. 45, iss. 9
• PID: 20.500.12556/RUL-143673
• UDK: 519.174.7
• ISSN pri članku: 1607-3606
• DOI: 10.2989/16073606.2021.1947919
• COBISS.SI-ID: 70914307
• Datum objave v RUL: 06.01.2023

Gradivo je del revije

• Naslov: Quaestiones mathematicae
• Skrajšan naslov: Quaest. math.
• Založnik: Taylor & Francis, National Inquiry Services Centre, South African Mathematical Society
• ISSN: 1607-3606
• COBISS.SI-ID: 514029849

Licence

• Licenca: CC BY-NC-ND 4.0, Creative Commons Priznanje avtorstva-Nekomercialno-Brez predelav 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by-nc-nd/4.0/deed.sl
• Opis: Najbolj omejujoča licenca Creative Commons. Uporabniki lahko prenesejo in delijo delo v nekomercialne namene in ga ne smejo uporabiti za nobene druge namene.

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: graf, barvanje, igra barvanja, neodvisna dominacijska igra, igralno kromatično število, drevo