5 papers
Arc-disjoint hamiltonian paths in Cartesian products of directed cycles
Iren Darijani, Babak Miraftab, Dave Witte Morris
We show that if and are directed cycles (of length at least two), then the Cartesian product has two arc-disjoint hamiltonian paths. (This answers a ques…
Canonical trees of tree-decompositions
Johannes Carmesin, Matthias Hamann, Babak Miraftab
We prove that every graph has a canonical tree of tree-decompositions that distinguishes all principal tangles (these include the ends and various kinds of large finite dense struc…
Two-ended quasi-transitive graphs
Babak Miraftab, Tim Rühmann
The well-known characterization of two-ended groups says that every two-ended group can be split over finite subgroups which means it is isomorphic to either by a free product with…
A Stallings' type theorem for quasi-transitive graphs
Matthias Hamann, Florian Lehner, Babak Miraftab +1
We consider infinite connected quasi-transitive locally finite graphs and show that every such graph with more than one end is a tree amalgamation of two other such graphs. This ca…
From cycles to circles in Cayley graphs
Babak Miraftab, Tim Rühmann
For locally finite infinite graphs the notion of Hamilton cycles can be extended to Hamilton circles, homeomorphic images of in the Freudenthal compactification. In this pape…