关于重圈的边色数

The Edge Chrometic Number of the Multiple Cycle

关于n-长重圈(即其基础简单图为n-长圈)C_n的边色数x′(C_n)。本文给出了 (ⅰ) X′(C_n)=△(C_n) (n=2k,k∈N) (ⅱ) X′(C_n)=△(C_n)+μ_0 (n=3) (ⅲ) X′(C_n)≤△(C_n)+[(μ_0)/k] (n=2k+1,k∈N)并且(ⅲ)中的不等式是上界可达的。(其中N表示自然数集合,μ_0是C_n的最小边重数,[x]表示不小于x的最小整数)。

In this paper the following results for multicycle of lengthn (namely, its fundamental simple graph is a cycle of length n) will be given: (ⅰ) X'(C_n)=Δ(C_n) (n=2k, k∈N) (ⅱ) X'(C_n)=Δ(C_n)+μ_0 (n= 3) (ⅲ) X'(C_n)≤Δ(C_n)+[μ_0/k] (n=2k+1, k∈N) and it will be shown that the equal-sign of the inequality in (ⅲ) is accessible. Where N denotes the set of natural numbers, μ_0 is the minimum of multiple numbers of edges of C_n, 「x(?)represents the minimum? of integers not less than x.