A POLYNOMIAL KERNEL FOR PROPER INTERVAL VERTEX DELETION

被引：30

作者：

Fomin, Fedor V. ^{[1
]}

Saurabh, Saket ^{[2
,3
]}

Villanger, Yngve ^{[1
]}

机构：

[1] Univ Bergen, Dept Informat, N-5008 Bergen, Norway

[2] Inst Math Sci, Madras 600113, Tamil Nadu, India

[3] Univ Bergen, N-5008 Bergen, Norway

来源：

SIAM JOURNAL ON DISCRETE MATHEMATICS | 2013年 / 27卷 / 04期

基金：

欧洲研究理事会;

关键词：

kernelization; parameterized complexity; proper interval graph; vertex deletion; sunflower lemma;

D O I：

10.1137/12089051X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

It is known that the problem of deleting at most k vertices to obtain a proper interval graph (Proper Interval Vertex Deletion) is fixed parameter tractable. However, whether the problem admits a polynomial kernel or not was open. Here, we answer this question in the affirmative by obtaining a polynomial kernel for Proper Interval Vertex Deletion. This resolves an open question of van Bevern et al. [Graph-Theoretic Concepts in Computer Science (WG 2010), Lecture Notes in Comput. Sci. 6410, Springer, Berlin, 2010, pp. 232-243].

引用

页码：1964 / 1976

页数：13

共 50 条

[31] Unit interval vertex deletion: Fewer vertices are relevant
Ke, Yuping
Cao, Yixin
Ouyang, Xiating
Li, Wenjun
Wang, Jianxin
JOURNAL OF COMPUTER AND SYSTEM SCIENCES, 2018, 95 : 109 - 121
[32] Polynomial kernels for PROPER INTERVAL COMPLETION and related problems
Bessy, Stephane
Perez, Anthony
INFORMATION AND COMPUTATION, 2013, 231 : 89 - 108
[33] A Polynomial Kernel for 3-Leaf Power Deletion
Ahn, Jungho
Eiben, Eduard
Kwon, O. -Joung
Oum, Sang-Il
ALGORITHMICA, 2023, 85 (10) : 3058 - 3087
[34] RECURSIVE FORMULA FOR CALCULATING THE CHROMATIC POLYNOMIAL OF A GRAPH BY VERTEX DELETION
许进
ActaMathematicaScientia, 2004, (04) : 577 - 582
[35] A Polynomial Kernel for 3-Leaf Power Deletion
Jungho Ahn
Eduard Eiben
O.-joung Kwon
Sang-il Oum
Algorithmica, 2023, 85 : 3058 - 3087
[36] Preprocessing for Outerplanar Vertex Deletion: An Elementary Kernel of Quartic Size
Donkers, Huib
Jansen, Bart M. P.
Wlodarczyk, Michal
ALGORITHMICA, 2022, 84 (11) : 3407 - 3458
[37] Preprocessing for Outerplanar Vertex Deletion: An Elementary Kernel of Quartic Size
Huib Donkers
Bart M. P. Jansen
Michał Włodarczyk
Algorithmica, 2022, 84 : 3407 - 3458
[38] A Polynomial Kernel for Deletion to the Scattered Class of Cliques and Trees
Jacob, Ashwin
Majumdar, Diptapriyo
Zehavi, Meirav
Leibniz International Proceedings in Informatics, LIPIcs, 322
[39] Recursive formula for calculating the chromatic polynomial of a graph by vertex deletion
Xu, J
ACTA MATHEMATICA SCIENTIA, 2004, 24 (04) : 577 - 582
[40] Faster algorithms and a smaller kernel for CLIQUES OR TREES VERTEX DELETION
Tsur, Dekel
INFORMATION PROCESSING LETTERS, 2025, 190

← 1 2 3 4 5 →