An exact algorithm for the channel assignment problem
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
List version of L(d, s)-labelings
Theoretical Computer Science - Graph colorings
The L(2, 1)-labelling of trees
Discrete Applied Mathematics
L(p, q)-labelling of K4-minor free graphs
Information Processing Letters
The 2-dipath chromatic number of Halin graphs
Information Processing Letters
Distance-two labelings of digraphs
Discrete Applied Mathematics
Labeling planar graphs with a condition at distance two
European Journal of Combinatorics
(2,1)-Total labelling of outerplanar graphs
Discrete Applied Mathematics
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Note: Improved upper bounds on the L(2,1) -labeling of the skew and converse skew product graphs
Theoretical Computer Science
Labelling planar graphs without 4-cycles with a condition on distance two
Discrete Applied Mathematics
Distance constrained labelings of planar graphs with no short cycles
Discrete Applied Mathematics
Graph labellings with variable weights, a survey
Discrete Applied Mathematics
An exact algorithm for the channel assignment problem
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
Note: The L(2,1)-labelling of trees
Discrete Applied Mathematics
L(p,q)-labelling of K4-minor free graphs
Information Processing Letters
Note: L(2,1)-Labelings on the composition of n graphs
Theoretical Computer Science
On the computational complexity of the L(2,1)-labeling problem for regular graphs
ICTCS'05 Proceedings of the 9th Italian conference on Theoretical Computer Science
Distance constrained labelings of graphs of bounded treewidth
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
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
Griggs and Yeh's Conjecture and $L(p,1)$-labelings
SIAM Journal on Discrete Mathematics
Labeling Planar Graphs without 4,5-Cycles with a Condition on Distance Two
SIAM Journal on Discrete Mathematics
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
List backbone colouring of graphs
Discrete Applied Mathematics
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A list channel assignment problem is a triple (G,L,w), where G is a graph, L is a function which assigns to each vertex of G a list of integers (colors), and w is a function which assigns to each edge of G a positive integer (its weight). A coloring c of the vertices of G is proper if c(v)\in L(v)$ for each vertex v and $|c(u)-c(v)|\ge w(uv)$ for each edge uv. A weighted degree $\deg_w(v)$ of a vertex v is the sum of the weights of the edges incident with v. If G is connected, $|L(v)|\deg_w(v)$ for at least one v, and $|L(v)|\ge\deg_w(v)$ for all v, then a proper coloring always exists. A list channel assignment problem is balanced if $|L(v)|=\deg_w(v)$ for all v. We characterize all balanced list channel assignment problems (G,L,w) which admit a proper coloring. An application of this result is that each graph with maximum degree $\Delta\ge 2$ has an L(2,1)-labeling using integers $0,\ldots,\Delta^2+\Delta-1$.