Ken-ichi Kawarabayashi

Finding topological subgraphs is fixed-parameter tractable

We prove that for every fixed undirected graph <i>H</i>, there is an O(|V(G)|³) time algorithm that, given a graph <i>G</i>, tests if <i>G</i> contains <i>H</i> as a topological subgraph (that is, a subdivision of <i>H</i> is subgraph of <i>G</i>). This shows that topological subgraph testing is fixed-parameter tractable, resolving a longstanding open question of Downey and Fellows from 1992. As a corollary, for every <i>H</i> we obtain an O(|V(G)|³) time algorithm that tests if there is an immersion of <i>H</i> into a given graph <i>G</i>. This answers another open question raised by Downey and Fellows in 1992.

On Sufficient Degree Conditions for a Graph to be

A graph is

k

k

-linked

-linked if for every list of

Shortest-path queries for complex networks: exploiting low tree-width outside the core

2k

Graph and map isomorphism and all polyhedral embeddings in linear time

vertices

Contraction decomposition in h-minor-free graphs and algorithmic applications

\{s_1,{\ldots}\,s_k, t_1,{\ldots}\,t_k\}

Estimating Local Intrinsic Dimensionality

, there exist internally disjoint paths

Linear min-max relation between the treewidth of H-minor-free graphs and its largest grid

P_1,{\ldots}\, P_k

A simpler algorithm and shorter proof for the graph minor decomposition

such that each