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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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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.
Real Number Channel Assignments for Lattices
, 2007
"... ... Portions of it have been obtained by other researchers for infinite regular lattices that model large planar networks. Here we present the complete function *(G; k, 1), for k> = 1 when G is the triangular, square, or hexagonal lattice. ..."
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Cited by 1 (0 self)
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... Portions of it have been obtained by other researchers for infinite regular lattices that model large planar networks. Here we present the complete function *(G; k, 1), for k> = 1 when G is the triangular, square, or hexagonal lattice.
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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Griggs and Yeh's conjecture . . .
, 2012
"... An L(p, 1)labeling 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)labeling f ..."
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An L(p, 1)labeling 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)labeling f is the difference between the largest and the smallest labels used by f. In 1992, Griggs and Yeh conjectured that every graph with maximum degree Δ 2 has an L(2, 1)labeling with span at most Δ2. We settle this conjecture for Δ sufficiently large. More generally, we show that for any positive integer p there exists a constant Δp such that every graph with maximum degree Δ Δp has an L(p, 1)labeling with span at most Δ2. This yields that for each positive integer p, there is an integer Cp such that every graph with maximum degree Δ has an L(p, 1)labeling with span at most Δ2 + Cp.