Improved Parameterized Algorithms for Cluster Vertex Deletion

In the Cluster Vertex Deletion problem, we are given a graph G and an integer k , and the goal is to determine whether we can delete at most k vertices from G to make the remaining graph a cluster graph, i.e., a graph in which every connected component is a complete graph. In this paper, we show tha...

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Vydáno v:Theory of computing systems Ročník 69; číslo 4; s. 37
Hlavní autoři: Tian, Kangyi, Xiao, Mingyu, Yang, Boting
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.12.2025
Springer Nature B.V
Témata:
Algorithms
Apexes
Cluster analysis
Clusters
Computer Science
Deletion
Graph theory
Graphs
Run time (computers)
Theory of Computation
Trees (mathematics)
ISSN:1432-4350, 1433-0490
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Shrnutí:In the Cluster Vertex Deletion problem, we are given a graph G and an integer k , and the goal is to determine whether we can delete at most k vertices from G to make the remaining graph a cluster graph, i.e., a graph in which every connected component is a complete graph. In this paper, we show that Cluster Vertex Deletion can be solved in time, improving the previous result of . To obtain this result, one crucial step is to show that Cluster Vertex Deletion on graphs of maximum degree at most 4 can be solved in time. For a general graph, after a series of reductions, if the maximum degree of the reduced graph is at most 4, we introduce a new technique, called core branching processing, to solve the problem; if the reduced graph has a vertex of degree at least 5, we adopt the previous method of automated generation of search trees to obtain the improved running time.
Bibliografie:ObjectType-Article-1
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ISSN:1432-4350
1433-0490
DOI:10.1007/s00224-025-10247-6