Labelling graphs with a condition at distance 2
SIAM Journal on Discrete Mathematics
Relating path coverings to vertex labellings with a condition at distance two
Discrete Mathematics
The $L(2,1)$-Labeling Problem on Graphs
SIAM Journal on Discrete Mathematics
A Theorem about the Channel Assignment Problem
SIAM Journal on Discrete Mathematics
Labeling the r-path with a condition at distance two
Discrete Applied Mathematics
k-L(2,1)-labelling for planar graphs is NP-complete for k≥4
Discrete Applied Mathematics
Fast exact algorithm for L(2, 1)-labeling of graphs
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
Exact λ-numbers of generalized Petersen graphs of certain higher-orders and on Möbius strips
Discrete Applied Mathematics
L(2,1) -labelling of generalized prisms
Discrete Applied Mathematics
IWOCA'11 Proceedings of the 22nd international conference on Combinatorial Algorithms
L(2,1)-labeling of dually chordal graphs and strongly orderable graphs
Information Processing Letters
Survey: Randomly colouring graphs (a combinatorial view)
Computer Science Review
Journal of Discrete Algorithms
Some results on the injective chromatic number of graphs
Journal of Combinatorial Optimization
On L(2,1)-labeling of generalized Petersen graphs
Journal of Combinatorial Optimization
Determining the l(2,1)-span in polynomial space
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
Determining the L(2,1)-span in polynomial space
Discrete Applied Mathematics
Fast exact algorithm for L(2,1)-labeling of graphs
Theoretical Computer Science
| Hi-index | 0.00 |
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(x, y) is the distance between the two vertices x and y 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 Δ ≥ 2 has an L(2, 1)-labelling with span at most Δ2 + 1. By settling this conjecture for Δ sufficiently large, we prove the existence of a constant C such that the span of any graph of maximum degree Δ is at most Δ 2 + C.