Conflict-Free Coloring And Related Problems

In order to improve the method for frequency distribution, Even et al. ([6]) and S. Smorodinsky ([12]) introduced the Conflict-Free coloring problems (CF-coloring for short). In this paper we give a systematical presentation of present results, including more general k-Conflict-Free coloring and k-Strong-Conflict-Free coloring, and online CF-coloring which is more close to practical usage. Based on these materials we get the exact values of several coloring numbers, and extend k-CF coloring to online case and give an estimate of the number of colors used.