The k - fold list coloring of cycles with Hall ’ s condition
نویسندگان
چکیده
We prove that any cycle Cn, n ≥ 4, with list assignment L, has a k -fold list coloring from the given lists if (i) each list contains at least 2k colors and (ii) Cn and L satisfy Hall’s condition for k -fold list colorings. Further, 2k in (i) cannot be replaced by 2k − 1 if either n is odd, or n is even and n ≥ k + 2. In other words, if n ≥ 4, the k -fold Hall number of a cycle Cn satifies h (Cn) ≤ 2k, with equality if n is odd, or n is even and n ≥ k + 2.
منابع مشابه
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