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- W2093443178 abstract "In the paper we consider a generalized vertex coloring model, namely T -coloring. For a given finite set T of nonnegative integers including 0, a proper vertex coloring is called a T -coloring if the distance of the colors of adjacent vertices is not an element of T . This problem is a generalization of the classic vertex coloring and appeared as a model of the frequency assignment problem. We present new results concerning the complexity of T -coloring with the smallest span on graphs with small degree Δ . We distinguish between the cases that appear to be polynomial or NP-complete. More specifically, we show that our problem is polynomial on graphs with Δ ⩽2 and in the case of k -regular graphs it becomes NP-hard even for every fixed T and every k >3. Also, the case of graphs with Δ =3 is under consideration. Our results are based on the complexity properties of the homomorphism of graphs." @default.
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- W2093443178 date "2003-08-01" @default.
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- W2093443178 title "The complexity of the T-coloring problem for graphs with small degree" @default.
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- W2093443178 doi "https://doi.org/10.1016/s0166-218x(02)00576-0" @default.
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