The Hardness of Embedding Grids and Walls

Yijia Chen; Martin Grohe; Bingkai Lin

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arXiv · 1703.06423

The Hardness of Embedding Grids and Walls

Yijia Chen·Martin Grohe·Bingkai Lin

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Abstract

The dichotomy conjecture for the parameterized embedding problem states that the problem of deciding whether a given graph $G$ from some class $K$ 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 $K$ 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 $K$ is the class of all grids or the class of all walls.

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Yijia Chen, Martin Grohe, Bingkai Lin. 2017-03-19. The Hardness of Embedding Grids and Walls. https://arxiv.org/abs/1703.06423

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