Labelling graphs with a condition at distance 2
SIAM Journal on Discrete Mathematics
Regular Article: Arrangements, Channel Assignments, and Associated Polynomials
Advances in Applied Mathematics
Improved algorithms for 3-coloring, 3-edge-coloring, and constraint satisfaction
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Fixed parameter complexity of λ-labelings
Discrete Applied Mathematics - special issue on the 25th international workshop on graph theoretic concepts in computer science (WG'99)
Deciding 3-Colourability in Less Than O(1.415^n) Steps
WG '93 Proceedings of the 19th International Workshop on Graph-Theoretic Concepts in Computer Science
A Theorem about the Channel Assignment Problem
SIAM Journal on Discrete Mathematics
On the span in channel assignment problems: bounds, computing and counting
Discrete Mathematics - Special issue: The 18th British combinatorial conference
3-coloring in time 0(1.3446^n): a no-MIS algorithm
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Colorings with few colors: counting, enumeration and combinatorial bounds
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
On the complexity of exact algorithm for L (2, 1)-labeling of graphs
Information Processing Letters
Channel assignment via fast zeta transform
Information Processing Letters
Distance three labelings of trees
Discrete Applied Mathematics
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A channel assignment problem is a triple (V,E,w) where V is a vertex set, E is an edge set and w is a function assigning edges positive integer weights. An assignment c of integers between 1 and K to the vertices is proper if |c(u)-c(v)|=w(uv) for each uv@?E; the smallest K for which there is a proper assignment is called the span. The input problem is set to be l-bounded if the values of w do not exceed l. We present an algorithm running in time O(n(l+2)^n) which outputs the span for l-bounded channel assignment problems with n vertices. An algorithm running in time O(nl(l+2)^n) for computing the number of different proper assignments of span at most K is further presented.