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L(2,1)labelling of graphs
 IN PROCEEDINGS OF THE ACMSIAM SYMPOSIUM ON DISCRETE ALGORITHM (SODA 2008
, 2008
"... An L(2, 1)labelling of a graph is a function f from the vertex set to the positive integers such that f(x) − f(y)  ≥ 2 if dist(x, y) = 1 and f(x) − f(y)  ≥ 1 if dist(x, y) = 2, where dist(u, v) is the distance between the two vertices u and v in the graph G. The span of an L(2, 1)labelli ..."
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Cited by 13 (3 self)
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An L(2, 1)labelling of a graph is a function f from the vertex set to the positive integers such that f(x) − f(y)  ≥ 2 if dist(x, y) = 1 and f(x) − f(y)  ≥ 1 if dist(x, y) = 2, where dist(u, v) is the distance between the two vertices u and v in the graph G. The span of an L(2, 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 at most ∆2 + 1. We settle this conjecture for ∆ sufficiently large.
Bounds for the real number graph labellings and application to labellings of the triangular lattice
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Distance Three Labelings of Trees∗
"... An L(2, 1, 1)labeling of a graph G assigns nonnegative integers to the vertices of G in such a way that labels of adjacent vertices differ by at least two, while vertices that are at distance at most three are assigned different labels. The maximum label used is called the span of the labeling, and ..."
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An L(2, 1, 1)labeling of a graph G assigns nonnegative integers to the vertices of G in such a way that labels of adjacent vertices differ by at least two, while vertices that are at distance at most three are assigned different labels. The maximum label used is called the span of the labeling, and the aim is to minimize this value. We show that the minimum span of an L(2, 1, 1)labeling of a tree can be bounded by a lower and an upper bound with difference one. Moreover, we show that deciding whether the minimum span attains the lower bound is an NPcomplete problem. This answers a known open problem, which was recently posed by King, Ras, and Zhou as well. We extend some of our results to general graphs and/or to more general distance constraints on the labeling. 1
Optimal real number graph labelings of a subfamily of Kneser graphs
, 2006
"... A notion of real number graph labelings captures the dependence of the span of an optimal channel assignment on the separations that are required between frequencies assigned to close transmitters. We determine the spans of such optimal labelings for a subfamily of Kneser graphs formed by the comple ..."
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Cited by 1 (1 self)
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A notion of real number graph labelings captures the dependence of the span of an optimal channel assignment on the separations that are required between frequencies assigned to close transmitters. We determine the spans of such optimal labelings for a subfamily of Kneser graphs formed by the complements of the line graphs of complete graphs. This subfamily contains (among others) the Petersen graph.
Determining the L(2, 1)span in polynomial space
 Discrete Appl. Math
, 2013
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IPFP6015964 AEOLUS Algorithmic Principles for Building Efficient Overlay Computers Deliverable D1.1.2
, 2007
"... 2.1 Treedepth and colorings of hypergraphs.................... 2 2.2 Fraternal augmentations, arrangeability and linear Ramsey numbers.... 3 ..."
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2.1 Treedepth and colorings of hypergraphs.................... 2 2.2 Fraternal augmentations, arrangeability and linear Ramsey numbers.... 3
L(p, 1)labelling of graphs
"... 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 ..."
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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
Griggs and Yeh's . . .
 SIAM JOURNAL ON DISCRETE MATHEMATICS, SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS, 2012, 26 (1), PP.145–168
, 2012
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