论文信息 - On-Line Coloring of Sparse Random Graphs and Random Trees

On-Line Coloring of Sparse Random Graphs and Random Trees

The performance of the greedy coloring algorithm “first fit” on sparse random graphsGn,c/nand on random trees is investigated. In each case, approximatelylog2logncolors are used, the exact number being concentrated almost surely on at most two consecutive integers for a sparse random graph and on at most three consecutive integers for a random tree.

Boris G. Pittel | Robert S. Weishaar

[1] J. Moon. Counting labelled trees , 1970 .

[2] Eli Upfal,et al. Sequential and Distributed Graph Coloring Algorithms with Performance Analysis in Random Graph Spaces , 1984, J. Algorithms.

[3] Joel H. Spencer,et al. Sharp concentration of the chromatic number on random graphsGn, p , 1987, Comb..

[4] Tomasz Łuczak. The chromatic number of random graphs , 1991 .

[5] Rajeev Motwani,et al. Randomized Algorithms , 1995, SIGA.

[6] András Gyárfás,et al. On-line and first fit colorings of graphs , 1988, J. Graph Theory.

[7] Tomasz Luczak. A note on the sharp concentration of the chromatic number of random graphs , 1991, Comb..

[8] Béla Bollobás,et al. The chromatic number of random graphs , 1988, Comb..

[9] Béla Bollobás,et al. Random Graphs , 1985 .

[10] Sandy Irani,et al. Coloring inductive graphs on-line , 1990, Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science.

[11] B. Pittel. On the probable behaviour of some algorithms for finding the stability number of a graph , 1982, Mathematical Proceedings of the Cambridge Philosophical Society.