Labelling graphs with a condition at distance 2
SIAM Journal on Discrete Mathematics
Labeling Chordal Graphs: Distance Two Condition
SIAM Journal on Discrete Mathematics
The $L(2,1)$-Labeling Problem on Graphs
SIAM Journal on Discrete Mathematics
On L(d, 1)-labelings of graphs
Discrete Mathematics
L(2,1)-labeling of planar graphs
DIALM '01 Proceedings of the 5th international workshop on Discrete algorithms and methods for mobile computing and communications
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
Fixed-Parameter Complexity of lambda-Labelings
WG '99 Proceedings of the 25th International Workshop on Graph-Theoretic Concepts in Computer Science
L(h,1)-labeling subclasses of planar graphs
Journal of Parallel and Distributed Computing
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This paper investigates a variant of the general problem of assigning channels to the stations of a wireless network when the graph representing the possible interferences is a matrogenic graph. In this problem, channels assigned to adjacent vertices must be at least two apart, while the same channel can be reused for vertices whose distance is at least three. Linear time algorithms are provided for matrogenic graphs and, in particular, for two specific subclasses: threshold graphs and split matrogenic graphs. For the first one of these classes the algorithm is exact, while for the other ones it approximates the optimal solution. Consequently, improvements on previously known results concerning subclasses of cographs, split graphs and graphs with diameter two are achieved.