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The property M(k) is a concept associated with the unique list coloring. A graph G has the property M(k) if for any collection of lists assigned to its vertices, each of size k, either there is no list coloring for G or there are at least two k-list colorings. The existing research results indicate that K1,1,1,r and K1⁎r,3 have the property M(3), and in addition K1⁎5,r and K1⁎r,5 have the property...
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