The Hardness of Embedding Grids and Walls

  • Yijia Chen
  • Martin Grohe
  • Bingkai LinEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10520)


The dichotomy conjecture for the parameterized embedding problem states that the problem of deciding whether a given graph G from some class \(\mathcal K\) of “pattern graphs” can be embedded into a given graph H (that is, is isomorphic to a subgraph of H) is fixed-parameter tractable if \(\mathcal K\) is a class of graphs of bounded tree width and \(W [1]\)-complete otherwise.

Towards this conjecture, we prove that the embedding problem is \(W [1]\)-complete if \(\mathcal K\) is the class of all grids or the class of all walls.



Yijia Chen is partially supported by the Sino-German Center for Research Promotion (CDZ 996) and National Nature Science Foundation of China (Project 61373029). Bingkai Lin is partially supported by the JSPS KAKENHI Grant (JP16H07409) and JST ERATO Grant (JPMJER1201) of Japan.


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Authors and Affiliations

  1. 1.School of Computer ScienceFudan UniversityShanghaiChina
  2. 2.Department of Computer ScienceRWTH Aachen UniversityAachenGermany
  3. 3.JST, ERATO, Kawarabayashi Large Graph ProjectNational Institute of InformaticsTokyoJapan

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