Fixed-Parameter Tractable Canonization and Isomorphism Test for Graphs of Bounded Treewidth

Restricted Space Algorithms for Isomorphism on Bounded Treewidth Graphs

The Graph Isomorphism problem restricted to graphs of bounded treewidth or bounded tree distance width are known to be solvable in polynomial time [2],[19]. We give restricted space algorithms for these problems proving the following results: • Isomorphism for bounded tree distance width graphs is in L and thus complete for the class. We also show that for this kind of graphs a canon can be com...

Fixed - parameter algorithms for minor - losed graphs ( of lo ally bounded treewidth ) ?

Embeddings of Graphs of Fixed Treewidth and Bounded Degree∗

Let F be any family of graphs of fixed treewidth and bounded degree. We construct a quadratic-time algorithm for calculating the genus distribution of the graphs in F . Within a post-order traversal of the decomposition tree, the algorithm involves a full-powered upgrading of production rules and root-popping. This algorithm for calculating genus distributions in quadratic time complements an a...

Subgraph Isomorphism , log - Bounded Fragmentation , and Graphs of ( Lo ally ) Bounded Treewidth ?

Recoloring bounded treewidth graphs

Let k be an integer. Two vertex k-colorings of a graph are adjacent if they differ on exactly one vertex. A graph is k-mixing if any proper k-coloring can be transformed into any other through a sequence of adjacent proper k-colorings. Any graph is (tw + 2)-mixing, where tw is the treewidth of the graph (Cereceda 2006). We prove that the shortest sequence between any two (tw + 2)-colorings is a...