Exploring the gap between treedepth and vertex cover through vertex integrity

For problems intractable on graphs of bounded treewidth, two graph parameters treedepth and vertex cover number have been used to obtain fine-grained algorithmic and complexity results. Although the studies in this direction are successful, we still need a systematic way for further investigations b...

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Bibliographic Details
Published in:Theoretical computer science Vol. 918; pp. 60 - 76
Main Authors: Gima, Tatsuya, Hanaka, Tesshu, Kiyomi, Masashi, Kobayashi, Yasuaki, Otachi, Yota
Format: Journal Article
Language:English
Published: Elsevier B.V 29.05.2022
Subjects:
Treedepth
Vertex cover number
Vertex integrity
Vertex integrity
Vertex cover number
Treedepth
ISSN:0304-3975, 1879-2294
Online Access:Get full text
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Summary:For problems intractable on graphs of bounded treewidth, two graph parameters treedepth and vertex cover number have been used to obtain fine-grained algorithmic and complexity results. Although the studies in this direction are successful, we still need a systematic way for further investigations because the graphs of bounded vertex cover number form a rather small subclass of graphs of bounded treedepth. To fill this gap, we use another graph parameter, vertex integrity, which is placed between the two parameters mentioned above. For several graph problems, we generalize fixed-parameter tractability results parameterized by vertex cover number to the ones parameterized by vertex integrity. We also show some finer complexity contrasts by showing hardness with respect to vertex integrity or treedepth.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2022.03.021