TY - JOUR

T1 - Exploring the gap between treedepth and vertex cover through vertex integrity

AU - Gima, Tatsuya

AU - Hanaka, Tesshu

AU - Kiyomi, Masashi

AU - Kobayashi, Yasuaki

AU - Otachi, Yota

N1 - Funding Information:
Partially supported by JSPS KAKENHI Grant Numbers JP18H04091 , JP18K11168 , JP18K11169 , JP19K21537 , JP20K19742 , JP20H05793 , JP21K11752 , JP21K17707 . A preliminary version appeared in the proceedings of the 12th International Conference on Algorithms and Complexity (CIAC 2021), Lecture Notes in Computer Science, vol. 12701, 2021, pp. 271–285.
Funding Information:
Partially supported by JSPS KAKENHI Grant Numbers JP18H04091, JP18K11168, JP18K11169, JP19K21537, JP20K19742, JP20H05793, JP21K11752, JP21K17707. A preliminary version appeared in the proceedings of the 12th International Conference on Algorithms and Complexity (CIAC 2021), Lecture Notes in Computer Science, vol. 12701, 2021, pp. 271?285.
Publisher Copyright:
© 2022 Elsevier B.V.

PY - 2022/5/29

Y1 - 2022/5/29

N2 - 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.

AB - 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.

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U2 - 10.1016/j.tcs.2022.03.021

DO - 10.1016/j.tcs.2022.03.021

M3 - Article

AN - SCOPUS:85126948621

SN - 0304-3975

VL - 918

SP - 60

EP - 76

JO - Theoretical Computer Science

JF - Theoretical Computer Science

ER -