Reconfiguring (non-spanning) arborescences

Reconfiguring spanning and induced subgraphs

Subgraph reconfiguration is a family of problems focusing on the reachability of the solution space in which feasible solutions are subgraphs, represented either as sets of vertices or sets of edges, satisfying a prescribed graph structure property. Although there has been previous work that can be categorized as subgraph reconfiguration, most of the related results appear under the name of the...

On packing spanning arborescences with matroid constraint

Let D = (V + s,A) be a digraph with a designated root vertex s. Edmonds’ seminal result [4] implies that D has a packing of k spanning s-arborescences if and only if D has a packing of k (s, t)-paths for all t ∈ V , where a packing means arc-disjoint subgraphs. Let M be a matroid on the set of arcs leaving s. A packing of (s, t)-paths is called M-based if their arcs leaving s form a base of M w...

Minimax regret spanning arborescences under uncertain costs

The paper considers a classical optimization problem on a network whose arc costs are partially known. It is assumed that an interval estimate is given for each arc cost and no further information about the statistical distribution of the truth value of the arc cost is known. In this context, given a spanning arborescence in the network, its cost can take on different values according to the ch...

Packing Algorithms for Arborescences (and Spanning Trees) in Capacitated Graphs

Packing Arborescences

In [7], Edmonds proved a fundamental theorem on packing arborescences that has become the base of several subsequent extensions. Recently, Japanese researchers found an unexpected further generalization which gave rise to many interesting questions about this subject [29], [20]. Another line of researches focused on covering intersecting families which generalizes Edmonds' theorems in a di eren...