Skip to main content
Theoretical Computer Science

Return to Answer

fixed broken link to springerlink.com; added full citation in tooltip; added link to M. kanté's answer; replaced "Kanté" with "kanté" to match that user's username: https://cstheory.stackexchange.com/users/4854/m-kanté
Source Link
edit approved Feb 27, 2023 at 9:45
user67557
edit approved Feb 27, 2023 at 9:45
user67557

As M. KantéM. kanté pointed out, it's open whether or not graph isomorphism is FPT when parameterized by tree-width. Furthermore, I don't believe there is any complexity-theoretic barrier to creating an FPT algorithm in this case.

For a survey of what's known about the fixed-parameter tractability of graph isomorphism, see the introduction of my paper with Anuj Dawar and Eryk Kopczyński herehere. In the paper we show graph isomorphism is FPT in the tree-depth of a graph, which is a necessary (but not sufficient) condition for graph isomorphism to be FPT in tree-width.

As M. Kanté pointed out, it's open whether or not graph isomorphism is FPT when parameterized by tree-width. Furthermore, I don't believe there is any complexity-theoretic barrier to creating an FPT algorithm in this case.

For a survey of what's known about the fixed-parameter tractability of graph isomorphism, see the introduction of my paper with Anuj Dawar and Eryk Kopczyński here. In the paper we show graph isomorphism is FPT in the tree-depth of a graph, which is a necessary (but not sufficient) condition for graph isomorphism to be FPT in tree-width.

As M. kanté pointed out, it's open whether or not graph isomorphism is FPT when parameterized by tree-width. Furthermore, I don't believe there is any complexity-theoretic barrier to creating an FPT algorithm in this case.

For a survey of what's known about the fixed-parameter tractability of graph isomorphism, see the introduction of my paper with Anuj Dawar and Eryk Kopczyński here. In the paper we show graph isomorphism is FPT in the tree-depth of a graph, which is a necessary (but not sufficient) condition for graph isomorphism to be FPT in tree-width.

Source Link
Adam Bouland
Adam Bouland
  • 743
  • 4
  • 10

As M. Kanté pointed out, it's open whether or not graph isomorphism is FPT when parameterized by tree-width. Furthermore, I don't believe there is any complexity-theoretic barrier to creating an FPT algorithm in this case.

For a survey of what's known about the fixed-parameter tractability of graph isomorphism, see the introduction of my paper with Anuj Dawar and Eryk Kopczyński here. In the paper we show graph isomorphism is FPT in the tree-depth of a graph, which is a necessary (but not sufficient) condition for graph isomorphism to be FPT in tree-width.