Fixed-parameter complexity of λ-labelings

A λ-labeling of a graph G is an assignment of labels from the set {0,…, λ} to the vertices of G such that vertices at distance of at most two get different labels and adjacent vertices get labels which are at least two apart. We study the minimum value λ= λ( G) such that G admits a λ-labeling. We sh...

Celý popis

Uloženo v:
Podrobná bibliografie
Vydáno v:Discrete Applied Mathematics Ročník 113; číslo 1; s. 59 - 72
Hlavní autoři: Fiala, Jiřı́, Kloks, Ton, Kratochvı́l, Jan
Médium: Journal Article Konferenční příspěvek
Jazyk:angličtina
Vydáno: Lausanne Elsevier B.V 2001
Amsterdam Elsevier
New York, NY
Témata:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Channel assignment
Computer science; control theory; systems
Exact sciences and technology
Fixed-parameter complexity
Graph cover
Graph labeling
Theoretical computing
Switzerland
Europe
Graph cover
Channel assignment
Graph labeling
Fixed-parameter complexity
Resource allocation
Channel allocation
Multigraph
NP complete problem
Graph theory
Workshop
Graph labelling
Overlay
1999
Complexity
ISSN:0166-218X, 1872-6771
On-line přístup:Získat plný text
Tagy: Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
Popis
Shrnutí:A λ-labeling of a graph G is an assignment of labels from the set {0,…, λ} to the vertices of G such that vertices at distance of at most two get different labels and adjacent vertices get labels which are at least two apart. We study the minimum value λ= λ( G) such that G admits a λ-labeling. We show that for every fixed value k⩾4 it is NP-complete to determine whether λ( G)⩽ k. We further investigate this problem for sparse graphs ( k-almost trees), extending the already known result for ordinary trees. In a generalization of this problem we wish to find a labeling such that vertices at distance two are assigned labels that differ by at least q and the labels of adjacent vertices differ by at least p. We denote the minimum λ that allows such a labeling by L( G; p, q). We show several hardness results for L( G; p, q) including that for any p> q⩾1 there is a λ= λ( p, q) such that deciding if L( G; p, q)⩽ λ is NP-complete, and that for p⩾2 q, this decision is NP-complete for every λ⩾ λ( p, q).
ISSN:0166-218X
1872-6771
DOI:10.1016/S0166-218X(00)00387-5