Hitting Topological Minor Models in Planar Graphs is Fixed Parameter Tractable

被引：0

作者：

Golovach, Petr A. ^{[1
]}

Stamoulis, Giannos ^{[2
]}

Thilikos, Dimitrios M. ^{[2
]}

机构：

[1] Univ Bergen, Dept Informat, N-5020 Bergen, Norway

[2] Univ Montpellier, CNRS, LIRMM, F-34000 Montpellier, France

来源：

ACM TRANSACTIONS ON ALGORITHMS | 2023年 / 19卷 / 03期

关键词：

Topological minors; irrelevant vertex technique; treewidth; vertex deletion problems; LINEAR-TIME ALGORITHMS; PATHS; COMPLEXITY; TREEWIDTH; SURFACE; GENUS;

D O I：

10.1145/3583688

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

For a finite collection of graphs F, the F -TM-Deletion problem has as input an n-vertex graph Gand an integer kand asks whether there exists a set S subset of V (G) with |S | <= k such that G \ S does not contain any of the graphs in F as a topological minor. We prove that for every such F, F -TM-Deletion is fixed parameter tractable on planar graphs. Our algorithm runs in a 2(O(k2)) center dot n(2) time, or, alternatively, in 2(O(k)) center dot n(4) time. Our techniques can easily be extended to graphs that are embeddable on any fixed surface.

引用

页数：29

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