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Title:Game chromatic number of Cartesian product graphs
Authors:ID Bartnicki, T. (Author)
ID Brešar, Boštjan (Author)
ID Grytczuk, J. (Author)
ID Kovše, Matjaž (Author)
ID Miechowicz, Z. (Author)
ID Peterin, Iztok (Author)
Files:URL http://www.combinatorics.org/Volume_15/PDF/v15i1r72.pdf
 
Language:English
Work type:Not categorized
Typology:1.01 - Original Scientific Article
Organization:FERI - Faculty of Electrical Engineering and Computer Science
Abstract:Obravnavamo igralno kromatično število chig kartezičnega produkta GBoxH dveh grafov G in H. Določimo točne vrednosti za chig(K2BoxH, ko je H pot, cikel ali poln graf. S pomočjo novo vpeljane "igre kombinacij" pokažemo, da igralno kromatično število ni omejeno znotraj razreda kartezičnih produktov dveh polnih dvodelnih grafov. Iz tega rezultata sledi, da igralno kromatično število chig(GBoxH ni navzgor omejeno s kako funkcijo igralnih kromatičnih števil grafov G in H. Analogen rezultat je izpeljan za igralno barvno število kartezičnih produktov grafov.
Keywords:matematika, teorija grafov, kartezični produkt grafov, igralno kromatično število, mathematics, graph theory, Cartesian prodict, game chromatic number
Year of publishing:2008
Number of pages:R72 (13 str.)
Numbering:Vol. 15, no. 1
PID:20.500.12556/DKUM-51675 New window
UDC:519.17
ISSN on article:1077-8926
COBISS.SI-ID:14761305 New window
NUK URN:URN:SI:UM:DK:B0JP2ZAP
Publication date in DKUM:10.07.2015
Views:1142
Downloads:265
Metadata:XML DC-XML DC-RDF
Categories:Misc.
:
BARTNICKI, T., BREŠAR, Boštjan, GRYTCZUK, J., KOVŠE, Matjaž, MIECHOWICZ, Z. and PETERIN, Iztok, 2008, Game chromatic number of Cartesian product graphs. The Electronic journal of combinatorics [online]. 2008. Vol. 15, no. 1. [Accessed 31 March 2025]. Retrieved from: http://www.combinatorics.org/Volume_15/PDF/v15i1r72.pdf
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Record is a part of a journal

Title:The Electronic journal of combinatorics
Shortened title:Electron. j. comb.
Publisher:N.J. Calkin and H.S. Wilf
ISSN:1077-8926
COBISS.SI-ID:6973785 New window

Secondary language

Language:Unknown
Title:Igralno kromatično število kartezičnih produktov grafov
Abstract:The game chromatic number chig is considered for the Cartesian product GBoxH of two graphs G and H. Exact values of chig(K2BoxH) are determined when H is a path, a cycle, or a complete graph. By using a newly introduced "game of combination" we show that the game chromatic number is not bounded in the class of Cartesian products of two complete bipartite graphs. This result implies that the game chromatic number chig(GBoxH) is not bounded from above by a function of game chromatic numbers of graphs G and H. An analogous result is derived for the game coloring number of the Cartesian product of graphs.


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