On the first-fit chromatic number of graphs

SIAM Journal on Discrete Mathematics

Volumn 22, Issue 3, 2008, Pages 887-900

  Balogh, József ^a   Hartke, Stephen G ^b   Liu, Qi ^a   Yu, Gexin ^c  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

^b UNIVERSITY OF NEBRASKA LINCOLN   (United States)

^c VANDERBILT UNIVERSITY   (United States)

Author keywords

Cartesian product; First fit chromatic number; Greedy coloring; Grundy coloring; Grundy number; Planar graph; Random graph

Indexed keywords

CARTESIAN PRODUCT; FIRST-FIT CHROMATIC NUMBER; GREEDY COLORING; GRUNDY COLORING; GRUNDY NUMBER; PLANAR GRAPH; RANDOM GRAPH;

COLORING;

GRAPH THEORY;

EID: 69649087621     PISSN: 08954801     EISSN: None     Source Type: Journal    
DOI: 10.1137/060672479     Document Type: Article

References (21)

1. N. Alon and J. H. Spencer, The Probabilistic Method, 2nd ed., John Wiley and Sons, New York, 2000.
2. B. Bollobás and P. Erdös, Cliques in random graphs, Math. Proc. Cambridge Philos. Soc., 80 (1976), pp. 419-427.
3. B. BollobAs, Random Graphs, 2nd ed., Cambridge Stud. Adv. Math. 73, Cambridge University Press, Cambridge, UK, 2001.
4. G. R. Brightwell, H. A. Kierstead, and W. T. Trotter, A Note on First-Fit Coloring of Interval Graphs, preprint, 2003.
5. C. A. Christen and S. M. Selkow, Some perfect coloring properties of graphs, J. Combin. Theory Ser. B, 27 (1979), pp. 49-59.
6. B. Effantin and H. Kheddouci, Grundy number of graphs, Discuss. Math. Graph Theory, 27 (2007), pp. 5-18.
7. P. Erdos, W. R. Hare, S. T. Hedetniemi, and R. Laskar, On the equality of Grundy and ochromatic number of graphs, J. Graph Theory, 11 (1987), pp. 157-159.
8. P. Erdos, S. T. Hedetniemi, R. C. Laskar, and C. E. Prins, On the equality of the partial Grundy and upper ochromatic numbers of graphs, Discrete Math., 272 (2003), pp. 53-64.
9. Z. Füredi, A. Gyárfás, G. N. Sárközy, and S. Selkow, Inequalities for the first-fit chromatic number, J. Graph Theory, to appear.
10. C. Germainian and H. Kheddouci, Grundy coloring for power graphs, Electron. Notes Discrete Math., 15 (2003), pp. 65-67.
11. G. R. Grimmett and C. J. H. McDiarmid, On colouring random graphs, Math. Proc. Cambridge Philos. Soc, 77 (1975), pp. 313-324.
12. D. G. Hoffman and P. D. Johnson, Jr., Greedy colorings and the Grundy chromatic number of the n-cube, Bull. Inst. Combin. Appl., 26 (1999), pp. 49-57.
13. P. M. Grundy, Mathematics and games, Eureka, 2 (1939), 6C-8.
14. S. IRANI, Coloring inductive graphs on-line, Algorithmica, 11 (1994), pp. 53-72.
15. H. A. Kierstead, The linearity of first-fit coloring of interval graphs, SIAM J. Discrete Math., 1 (1988), pp. 526-530.
16. H. A. Kierstead and J. Qin, Coloring interval graphs with first-fit, Discrete Math., 144 (1995), pp. 47-57.
17. H. A. Kierstead and W. T. Trotter, private communication.
18. C. J. H. McDiarmid, Colouring random graphs badly, in Graph Theory and Combinatorics, Res. Notes in Math. 34, R. J. Wilson, ed., Pitman, Boston, 1979, pp. 76-86.
19. S. Pemmaraju, R. Raman, and K. Varadarajan, Buffer minimization using max-coloring, in Proceedings of the 15th Annual ACM-SIAM Symposium on Discrete Algorithms, New Orleans, LA, SIAM, Philadelphia, 2004, pp. 562-571.
20. D. R. Woodall, Problem No. 4, in Proceedings of the British Combinatorial Conference 1973, London Math. Soc, Lecture Note Series 13, Cambridge University Press, 1974.
21. M. Zaker, Results on the Grundy chromatic number of graphs, Discrete Math., 306 (2006), pp. 3166-3173.