T-colorings of graphs: recent results and open problems
Discrete Mathematics - Special issue: advances in graph labelling
No-hole (r + 1)-distant colorings
Discrete Mathematics
Extremal problems on consecutive L(2,1)-labelling
Discrete Applied Mathematics
Distance-two labellings of Hamming graphs
Discrete Applied Mathematics
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In this paper, we introduce a variant of graph coloring which is motivated by the channel assignment problem. In this variant, called no-hole 2-distant coloring, we seek to color the vertices of a graph with positive integers so that two adjacent vertices get integers which differ by more than 1 (the 2-distant requirement) and so that the set of integers used as colors is a consecutive set (the no-hole requirement). We study the question of what graphs have such colorings. We also study the question of what graphs have such colorings which are near-optimal in the sense that the span, or separation between the largest and smallest colors used, is no more than one larger than the minimum span in a non-adjacent coloring which may have holes.