منابع مشابه
Limited Packings in Graphs
A set of sensors is to be deployed to covertly monitor a facility. If too many sensors are placed close to any given location in the facility, then it is likely the presence of the sensors will be detected. Where then should the sensors be placed so that the total number we deploy is maximized while at the same time we avoid placing some threshold number close to any given location? There are m...
متن کاملBounds and algorithms for limited packings in graphs
We consider (closed neighbourhood) packings and their generalization in graphs called limited packings. A vertex set X in a graphG is a k-limited packing if for any vertex v ∈ V (G), |N [v] ∩X | ≤ k, where N [v] is the closed neighbourhood of v. The k-limited packing number Lk(G) is the largest size of a k-limited packing in G. Limited packing problems can be considered as secure facility locat...
متن کاملThe probabilistic approach to limited packings in graphs
We consider (closed neighbourhood) packings and their generalization in graphs. A vertex set X in a graph G is a k-limited packing if for any vertex v ∈ V (G), |N [v] ∩X| ≤ k, where N [v] is the closed neighbourhood of v. The k-limited packing number Lk(G) of a graph G is the largest size of a k-limited packing in G. Limited packing problems can be considered as secure facility location problem...
متن کاملPackings in Complete Graphs
We deal with the concept of packings in graphs, which may be regarded as a generalization of the theory of graph design. In particular we construct a vertexand edge-disjoint packing of Kn (where n 2 mod 4 equals 0 or 1) with edges of different cyclic length. Moreover we consider edge-disjoint packings in complete graphs with uniform linear forests (and the resulting packings have special additi...
متن کاملOn Perfect Packings in Dense Graphs
We say that a graph G has a perfect H-packing if there exists a set of vertex-disjoint copies of H which cover all the vertices in G. We consider various problems concerning perfect Hpackings: Given n, r,D ∈ N, we characterise the edge density threshold that ensures a perfect Kr-packing in any graph G on n vertices and with minimum degree δ(G) ≥ D. We also give two conjectures concerning degree...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Optimization
سال: 2020
ISSN: 1382-6905,1573-2886
DOI: 10.1007/s10878-020-00606-z