Partitioning graphs into connected parts
نویسندگان
چکیده
منابع مشابه
Partitioning Graphs into Connected Parts
The 2-Disjoint Connected Subgraphs problem asks if a given graph has two vertex-disjoint connected subgraphs containing prespecified sets of vertices. We show that this problem is NP-complete even if one of the sets has cardinality 2. The Longest Path Contractibility problem asks for the largest integer ` for which an input graph can be contracted to the path P` on ` vertices. We show that the ...
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We show that two results on covering of edge colored graphs by monochromatic connected parts can be extended to partitioning. We prove that for any 2-edgecolored non-trivial r-uniform hypergraph H, the vertex set can be partitioned into at most α(H)− r+ 2 monochromatic connected parts, where α(H) is the maximum size of a set of vertices that does not contain any edge. In particular, any 2-edgec...
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A graph G is arbitrarily partitionable (AP for short) if for every partition (n1, n2, ..., np) of |V (G)| there exists a partition (V1, V2, ..., Vp) of V (G) such that each Vi induces a connected subgraph of G with order ni. If, additionally, k of these subgraphs (k ≤ p) each contains an arbitrary vertex of G prescribed beforehand, then G is arbitrarily partitionable under k prescriptions (AP+k...
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For positive integer k and finite set X we define a k-partition of X as a partition X=X,UX,U..-UX, where IX,1 =k for i=l,2,...,p. For a graph property rr we define a &-partition of the vertices or edges to be one in which each subset induces a graph with property rr. Thus for example a connected-k-partition of I/or E is a k-partition of V or E for which each subset induces a connected subgraph....
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Clustering is a well-known and important problem with numerous applications. The graph-based model is one of the typical cluster models. In the graph model, clusters are generally defined as cliques. However, such an approach might be too restrictive as in some applications, not all objects from the same cluster must be connected. That is why different types of cliques relaxations often conside...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2009
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2009.06.028