Colouring game and generalized colouring game on graphs with cut-vertices

Elżbieta Sidorowicz

Discussiones Mathematicae Graph Theory (2010)

  • Volume: 30, Issue: 3, page 499-533
  • ISSN: 2083-5892

Abstract

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For k ≥ 2 we define a class of graphs 𝓗 ₖ = {G: every block of G has at most k vertices}. The class 𝓗 ₖ contains among other graphs forests, Husimi trees, line graphs of forests, cactus graphs. We consider the colouring game and the generalized colouring game on graphs from 𝓗 ₖ.

How to cite

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Elżbieta Sidorowicz. "Colouring game and generalized colouring game on graphs with cut-vertices." Discussiones Mathematicae Graph Theory 30.3 (2010): 499-533. <http://eudml.org/doc/270790>.

@article{ElżbietaSidorowicz2010,
abstract = {For k ≥ 2 we define a class of graphs 𝓗 ₖ = \{G: every block of G has at most k vertices\}. The class 𝓗 ₖ contains among other graphs forests, Husimi trees, line graphs of forests, cactus graphs. We consider the colouring game and the generalized colouring game on graphs from 𝓗 ₖ.},
author = {Elżbieta Sidorowicz},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {colouring game; generalized colouring game},
language = {eng},
number = {3},
pages = {499-533},
title = {Colouring game and generalized colouring game on graphs with cut-vertices},
url = {http://eudml.org/doc/270790},
volume = {30},
year = {2010},
}

TY - JOUR
AU - Elżbieta Sidorowicz
TI - Colouring game and generalized colouring game on graphs with cut-vertices
JO - Discussiones Mathematicae Graph Theory
PY - 2010
VL - 30
IS - 3
SP - 499
EP - 533
AB - For k ≥ 2 we define a class of graphs 𝓗 ₖ = {G: every block of G has at most k vertices}. The class 𝓗 ₖ contains among other graphs forests, Husimi trees, line graphs of forests, cactus graphs. We consider the colouring game and the generalized colouring game on graphs from 𝓗 ₖ.
LA - eng
KW - colouring game; generalized colouring game
UR - http://eudml.org/doc/270790
ER -

References

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  1. [1] S.D. Andres, The game chromatic index of forests of maximum degree Δ ≥ 5, Discrete Applied Math. 154 (2006) 1317-1323, doi: 10.1016/j.dam.2005.05.031. Zbl1091.05023
  2. [2] H.L. Bodlaender, On the complexity of some colouring games, Internat. J. Found. Comput. Sci. 2 (1991) 133-148, doi: 10.1142/S0129054191000091. Zbl0753.05061
  3. [3] M. Borowiecki and P. Mihók, Hereditary properties of graphs, in: V.R. Kulli, ed(s), Advances in Graph Theory Vishwa International Publication Gulbarga, 1991) 41-68. 
  4. [4] M. Borowiecki and E. Sidorowicz, Generalized game colouring of graphs, Discrete Math. 307 (2007) 1225-1231, doi: 10.1016/j.disc.2005.11.060. Zbl1118.05030
  5. [5] L. Cai and X. Zhu, Game chromatic index of k-degenerate graphs, J. Graph Theory 36 (2001) 144-155, doi: 10.1002/1097-0118(200103)36:3<144::AID-JGT1002>3.0.CO;2-F Zbl0966.05028
  6. [6] G. Chartrand and L. Leśniak, Graphs and Digraphs (Fourth Edition Chapman & Hall/CRC, 2005). Zbl1057.05001
  7. [7] Ch. Chou, W. Wang and X. Zhu, Relaxed game chromatic number of graphs, Discrete Math. 262 (2003) 89-98, doi: 10.1016/S0012-365X(02)00521-6. Zbl1012.05067
  8. [8] T. Dinski and X. Zhu, A bound for the game chromatic number of graphs, Discrete Math. 196 (1999) 109-115, doi: 10.1016/S0012-365X(98)00197-6. Zbl0928.05022
  9. [9] C. Dunn and H.A. Kierstead, The relaxed game chromatic number of outerplanar graphs, J. Graph Theory 46 (2004) 69-106, doi: 10.1002/jgt.10172. Zbl1042.05038
  10. [10] P.L. Erdös, U. Faigle, W. Hochstättler and W. Kern, Note on the game chromatic index of trees, Theoretical Computer Science 313 (2004) 371-376, doi: 10.1016/j.tcs.2002.10.002. Zbl1066.91015
  11. [11] U. Faigle, U. Kern, H.A. Kierstead and W.T. Trotter, On the game chromatic number of some classes of graphs, Ars Combin. 35 (1993) 143-150. Zbl0796.90082
  12. [12] D. Guan and X. Zhu, The game chromatic number of outerplanar graphs, J. Graph Theory 30 (1999) 67-70, doi: 10.1002/(SICI)1097-0118(199901)30:1<67::AID-JGT7>3.0.CO;2-M Zbl0929.05032
  13. [13] W. He, J. Wu and X. Zhu, Relaxed game chromatic number of trees and outerplanar graphs, Discrete Math. 281 (2004) 209-219, doi: 10.1016/j.disc.2003.08.006. Zbl1042.05042
  14. [14] H.A. Kierstead, A simple competitive graph colouring algorithm, J. Combin. Theory (B) 78 (2000) 57-68, doi: 10.1006/jctb.1999.1927. Zbl1024.05029
  15. [15] H.A. Kierstead and Zs. Tuza, Marking games and the oriented game chromatic number of partial k-trees, Graphs Combin. 19 (2003) 121-129, doi: 10.1007/s00373-002-0489-5. 
  16. [16] E. Sidorowicz, The game chromatic number and the game colouring number of cactuses, Information Processing Letters 102 (2007) 147-151, doi: 10.1016/j.ipl.2006.12.003. Zbl1185.91058
  17. [17] J. Wu and X. Zhu, Lower bounds for the game colouring number of planar graphs and partial k-trees, Discrete Math. 308 (2008) 2637-2642, doi: 10.1016/j.disc.2007.05.023. Zbl1142.05032
  18. [18] J. Wu and X. Zhu, Relaxed game chromatic number of outerplanar graphs, Ars Combin. 81 (2006) 359-367. Zbl1174.05378
  19. [19] D. Yang and H.A. Kierstead, Asymmetric marking games on line graphs, Discrete Math. 308 (2008) 1751-1755, doi: 10.1016/j.disc.2007.03.082. Zbl1136.05022
  20. [20] X. Zhu, The Game Colouring Number of Planar Graphs, J. Combin. Theory (B) 75 (1999) 245-258, doi: 10.1006/jctb.1998.1878. Zbl0933.05052
  21. [21] X. Zhu, Game colouring number of pseudo partial k-trees, Discrete Math. 215 (2000) 245-262, doi: 10.1016/S0012-365X(99)00237-X. 
  22. [22] X. Zhu, Refined activation strategy for the marking game, J. Combin. Theory (B) 98 (2008) 1-18 Zbl1127.05047

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