On the complexity of H-coloring
Journal of Combinatorial Theory Series B
T-colorings of graphs: recent results and open problems
Discrete Mathematics - Special issue: advances in graph labelling
Discrete Mathematics - Special volume (part two) to mark the centennial of Julius Petersen's “Die theorie der regula¨ren graphs” (“The theory of regular graphs”)
The channel assignment problem for mutually adjacent sites
Journal of Combinatorial Theory Series A
Further Results on T-Coloring and Frequency Assignment Problems
SIAM Journal on Discrete Mathematics
A rainbow about T-colorings for complete graphs
Discrete Mathematics
T-graphs and the channel assignment problem
Discrete Mathematics
Distance graphs and the T-coloring problem
Discrete Mathematics
Divisibility and T-span of graphs
Discrete Mathematics
Free bits, PCPs and non-approximability-towards tight results
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
A polynomial algorithm for finding T-span of generalized cacti
Discrete Applied Mathematics
Colour reassignment in tabu search for the graph set t-colouring problem
HM'06 Proceedings of the Third international conference on Hybrid Metaheuristics
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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.