The list extremal number f（G） is defined for a graph G as the smallest integer k such that the join of G with a stable set of size k is not ｜V（G）｜-choosable. In this paper, we find the exact value of f（G）, where G is the union of edge-disjoint cycles of length three, four, five and six. Our results confirm two conjectures posed by S. Gravier, F. Maffray and B. Mohar.
The incidence chromatic number of G is the least number of colors such that G has an incidence coloring. It is proved that the incidence chromatic number of Cn^p, the p-th power of the circuit graph, is 2p ＋ 1 if and only if n = k（2p ＋ 1）, for other cases： its incidence chromatic number is at most 2p ＋ [r/k] ＋ 2, where n = k（p ＋ 1） ＋ r, k is a positive integer. This upper bound is tight for some cases.
