Finding k Disjoint Triangles in an Arbitrary Graph

We consider the NP-complete problem of deciding whether an input graph on n vertices has k vertex-disjoint copies of a fixed graph H. For H=K3 (the triangle) we give an O(22klog k + 1.869kn2) algorithm, and for general H an O(2k|H|logk + 2k|H|log |H|n|H|) algorithm. We introduce a preprocessing (ker...

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Bibliographic Details
Published inGraph-Theoretic Concepts in Computer Science pp. 235 - 244
Main Authors Fellows, Mike, Heggernes, Pinar, Rosamond, Frances, Sloper, Christian, Telle, Jan Arne
Format Book Chapter Conference Proceeding
LanguageEnglish
Published Berlin, Heidelberg Springer Berlin Heidelberg 01.01.2004
Springer
SeriesLecture Notes in Computer Science
Subjects
Applied sciences
Arbitrary Graph
Computer science; control theory; systems
Exact Algorithm
Exact sciences and technology
Information retrieval. Graph
Input Graph
Reduction Rule
Search Tree
Theoretical computing
Graph decomposition
NP complete problem
Graph theory
Kernel method
Polynomial time
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ISBN9783540241324
3540241329
ISSN0302-9743
1611-3349
DOI10.1007/978-3-540-30559-0_20

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Summary:We consider the NP-complete problem of deciding whether an input graph on n vertices has k vertex-disjoint copies of a fixed graph H. For H=K3 (the triangle) we give an O(22klog k + 1.869kn2) algorithm, and for general H an O(2k|H|logk + 2k|H|log |H|n|H|) algorithm. We introduce a preprocessing (kernelization) technique based on crown decompositions of an auxiliary graph. For H=K3 this leads to a preprocessing algorithm that reduces an arbitrary input graph of the problem to a graph on O(k3) vertices in polynomial time.
Bibliography:This work was initiated while the first and third authors were visiting the University of Bergen.
ISBN:9783540241324
3540241329
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-540-30559-0_20