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...

Full description

Saved in:
Bibliographic Details
Published in:Theory of computing systems Vol. 69; no. 4; p. 37
Main Authors: Tian, Kangyi, Xiao, Mingyu, Yang, Boting
Format: Journal Article
Language:English
Published: New York Springer US 01.12.2025
Springer Nature B.V
Subjects:
Algorithms
Apexes
Cluster analysis
Clusters
Computer Science
Deletion
Graph theory
Graphs
Run time (computers)
Theory of Computation
Trees (mathematics)
ISSN:1432-4350, 1433-0490
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1432-4350
1433-0490
DOI:10.1007/s00224-025-10247-6