کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4650850 | 1342506 | 2007 | 8 صفحه PDF | دانلود رایگان |

The notion of the list-T-coloring is a common generalization of the T-coloring and the list-coloring. Given a set of non-negative integers T, a graph G and a list-assignment L, the graph G is said to be T-colorable from the list-assignment L if there exists a coloring c such that the color c(v)c(v) of each vertex vv is contained in its list L(v)L(v) and |c(u)-c(v)|∉T|c(u)-c(v)|∉T for any two adjacent vertices u and vv. The T-choice number of a graph G is the minimum integer k such that G is T-colorable for any list-assignment L which assigns each vertex of G a list of at least k colors.We focus on list-T-colorings with infinite sets T. In particular, we show that for any fixed set T of integers, all graphs have finite T-choice number if and only if the T -choice number of K2K2 is finite. For the case when the T -choice number of K2K2 is finite, two upper bounds on the T-choice number of a graph G are provided: one being polynomial in the maximum degree of the graph G, and the other being polynomial in the T -choice number of K2K2.
Journal: Discrete Mathematics - Volume 307, Issue 23, 6 November 2007, Pages 3040–3047