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Indicated coloring game on Cartesian products of graphsBrešar, Boštjan ; Jakovac, Marko ; Mesarič Štesl, DašaThe indicated coloring game is played on a simple graph ▫$G$▫ by two players, with a fixed set ▫$C$▫ of colors. In each round of the game Ann indicates an uncolored vertex, and Ben colors it using a ... color from ▫$C$▫, obeying just the proper coloring rule. The goal of Ann is to achieve a proper coloring of the whole graph, while Ben is trying to prevent this. The minimum cardinality of the set of colors ▫$C$▫ for which Ann has a winning strategy is called the indicated chromatic number, ▫$ \chi_i ( G )$▫, of a graph ▫$G$▫. In this paper, we prove that the indicated chromatic number of the Cartesian product ▫$G \square K_{n , m}$▫ is equal to 3 if ▫$\chi_i ( G ) = 3$▫. We also prove that ▫$\chi_i ( G \square T ) = \chi ( G )$▫, where ▫$G$▫ is a block graph and ▫$T$▫ is a tree. Indicated colorings in some other classes of Cartesian products of graphs are also studied. The investigations lead us to propose a Sabidussi-type equality as an open problem.Source: Discrete applied mathematics. - ISSN 0166-218X (Vol. 289, Jan. 2021, str. 320-326)Type of material - article, component part ; adult, seriousPublish date - 2021Language - englishCOBISS.SI-ID - 41803267
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Author | Brešar, Boštjan ; Jakovac, Marko ; Mesarič Štesl, Daša |
Title | Indicated coloring game on Cartesian products of graphs |
Publication date | 2020-11-19 |
COBISS.SI-ID | 41803267 |
Publication version in repository | Unidentified |
Publication licence | Unidentified |
Embargo | Unidentified |
Project(s) from which the publication was funded
Title | Acronym | Project ID | Funder |
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Teorija grafov | P1-0297-2022 |
Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije |
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Sodobne invariante grafov | J1-9109-2018 |
Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije |
|
Sodobni in novi metrični koncepti v teoriji grafov | J1-1693-2019 |
Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije |
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Brešar, Boštjan | 17005 |
Jakovac, Marko | 29919 |
Mesarič Štesl, Daša | 51477 |
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