The monadic second-order logic of graphs. I. recognizable sets of finite graphs
Information and Computation
Labelling graphs with a condition at distance 2
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
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)
Invitation to Discrete Mathematics
Invitation to Discrete Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Distance Constrained Labeling of Precolored Trees
ICTCS '01 Proceedings of the 7th Italian Conference on Theoretical Computer Science
The L(h, k)-Labelling Problem: A Survey and Annotated Bibliography
The Computer Journal
Complexity of Partial Covers of Graphs
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
Systems of distant representatives
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
Distance constrained labelings of graphs of bounded treewidth
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
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An H(p, q)-labeling of a graph G is a vertex mapping f : VG → VH such that the distance between f(u) and f(v) (measured in the graph H) is at least p if the vertices u and v are adjacent in G, and the distance is at least q if u and v are at distance two in G. This notion generalizes the notions of L(p, q)- and C(p, q)-labelings of graphs studied as particular graph models of the Frequency Assignment Problem. We study the computational complexity of the problem of deciding the existence of such a labeling when the graphs G and H come from restricted graph classes. In this way we extend known results for linear and cyclic labelings of trees, with a hope that our results would help to open a new angle of view on the still open problem of L(p, q)-labeling of trees for fixed p q 1 (i.e., when G is a tree and H is a path). We present a polynomial time algorithm for H(p, 1)-labeling of trees for arbitrary H. We show that the H(p, q)-labeling problem is NP-complete when the graph G is a star. As the main result we prove NP-completeness for H(p, q)-labeling of trees when H is a symmetric q-caterpillar.