J un 1 99 9 On Uniquely List Colorable Graphs ∗
نویسنده
چکیده
Let G be a graph with n vertices and suppose that for each vertex v in G, there exists a list of k colors, L(v), such that there is a unique proper coloring for G from this collection of lists, then G is called a uniquely k–list colorable graph. Recently M. Mahdian and E.S. Mahmoodian characterized uniquely 2–list colorable graphs. Here we state some results which will pave the way in characterization of uniquely k–list colorable graphs. There is a relationship between this concept and defining sets in graph colorings and critical sets in latin squares.
منابع مشابه
J un 1 99 9 Some Concepts in List Coloring
In this paper uniquely list colorable graphs are studied. A graph G is called to be uniquely k–list colorable if it admits a k–list assignment from which G has a unique list coloring. The minimum k for which G is not uniquely k–list colorable is called the m–number of G. We show that every triangle–free uniquely colorable graph with chromatic number k+1, is uniquely k–list colorable. A bound fo...
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Let G be a graph with ν vertices, and let S1, S2, . . . , Sν be a list of colors on its vertices, each of size k. If there exists a unique proper coloring for G from this list of colors, then G is called uniquely k–list colorable graph. We characterize all uniquely 2–list colorable graphs, and discuss uniquely k–list colorable graphs by introducing some open problems. We also show the connectio...
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Let G be a graph with n vertices and suppose that for each vertex v in G, there exists a list of k colors, L(v), such that there is a unique proper coloring for G from this collection of lists, then G is called a uniquely k–list colorable graph. Recently M. Mahdian and E.S. Mahmoodian characterized uniquely 2–list colorable graphs. Here we state some results which will pave the way in character...
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