@MISC{Havet_l(p,1)-labelling, author = {Frédéric Havet and Bruce Reed and Jean-Sébastien Sereni}, title = {L(p, 1)-labelling of graphs}, year = {} }

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Abstract

An L(p, 1)-labelling of a graph is a function f from the vertex set to the positive integers such that |f(x) − f(y) | ≥ p if dist(x, y) = 1 and |f(x) − f(y) | ≥ 1 if dist(x, y) = 2, where dist(x, y) is the distance between the two vertices x and y in the graph. The span of an L(p, 1)labelling f is the difference between the largest and the smallest labels used by f plus 1. In 1992, Griggs and Yeh conjectured that every graph with maximum degree ∆ ≥ 2 has an L(2, 1)-labelling with span