A general upper bound on the list chromatic number of locally sparse graphs

Combinatorics Probability and Computing

Volumn 11, Issue 1, 2002, Pages 103-111

  Vu, Van H ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL METHODS; MATHEMATICAL MODELS; NUMERICAL METHODS; THEOREM PROVING;

CHROMATIC INDEX; CHROMATIC NUMBERS; MULTIPLICATIVE CONSTANT; SPARSE GRAPHS;

GRAPH THEORY;

EID: 0036003898     PISSN: 09635483     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0963548301004898     Document Type: Article

References (18)

1. Alon, N. (1993) Restricted colorings of graphs. In Survey in Combinatorics (Proc. 14th British Combinatorial Conference), Vol. 187 of London Mathematical Society Lecture Notes Series (K. Walker, ed.), Cambridge University Press, pp. 1-33.
2. Alon, N. and Spencer, J. (1992) The Probabilistic Method, Wiley, New York.
3. Alon, N., Krivelevich, M. and Sudakov, B. (1999) Coloring graphs with sparse neighborhoods. J. Combin. Theory Ser. B 77 33-82.
4. Bollobás, B. (1985) Random Graphs, Academic Press, London.
5. Erdo″s, P., Rubin, A. L. and Taylor, H. (1979) Choosability in graphs. In Proc. West Coast Conf. on Combinatorics, Graph Theory and Computing, Vol. XXVI of Congressus Numerantium, pp. 125-157.
6. Faudree, R., Gyárfás, A., Schelp, R. and Tuza, Z. (1990) The strong chromatic index of graphs. Ars Combinatorica 29B 205-211.
7. Johansson, A. (1996) Asymptotic choice number for triangle free graphs. DIMACS Technical Report 91-95.
8. Kahn, J. (1996) Asymptotically good list-colorings. J. Combin. Theory Ser. A 73 1-59.
9. Kim, J. H. (1995) On Brooks' theorem for sparse graphs. Combin. Probab. Comput. 4 97-132.
10. Kostochka, A. and Steibitz, M. (2000) On the number of edges in color-critical graphs and hypergraphs. Combinatorica 20 521-530.
11. Krivelevich, M., Sudakov, B., Vu, V. H. and Wormald, N. (2001) Random regular graphs of high degree. Random Struct. Algorithms 18 346-363.
12. Lovász, L. (1993) Combinatorial Problems and Exercises, 2nd edn, North-Holland.
13. Mahdian, M. (2000) The strong chromatic index of graphs. Random Struct. Algorithms 17 357-375.
14. Molloy, M. and Reed, B. (1997) A bound on the strong chromatic index of a graph. J. Combin. Theory Ser. B 69 103-109.
15. Molloy, M. and Reed, B. Monograph in preparation.
16. Tuza, Z. (1997) Graph coloring with local constraints: A survey. Discuss Math. Graph Theory 17 161-228.
17. Vizing, V. G. (1976) Coloring the vertices of a graph in prescribed colors (in Russian). Diskret. Analiz. No. 29, Metody Diskret. Anal. v. Teorii Kodov i Shem 101 3-10.
18. Vu, V. H. (1999) On some degree conditions which guarantee the upper bound of chromatic (choice) number of random graphs. J. Graph Theory 31 201-226.