Summarizing Graph Data Via the Compactness of Disjoint Paths

Shortest k-Disjoint Paths via Determinants

The well-known k-disjoint path problem (k-DPP) asks for pairwise vertex-disjoint paths between k specified pairs of vertices (si, ti) in a given graph, if they exist. The decision version of the shortest k-DPP asks for the length of the shortest (in terms of total length) such paths. Similarly the search and counting versions ask for one such and the number of such shortest set of paths, respec...

Finding k Disjoint Paths in a Directed Planar Graph

We show that for each fixed k, the problem of finding k pairwise vertex-disjoint directed paths between given pairs of terminals in a directed planar graph is solvable in polynomial time.

FINDING k PARTIALLY DISJOINT PATHS IN A DIRECTED PLANAR GRAPH

The partially disjoint paths problem is: given: a directed graph, vertices r1, s1, . . . , rk, sk, and a set F of pairs {i, j} from {1, . . . , k}, find: for each i = 1, . . . , k a directed ri − si path Pi such that if {i, j} ∈ F then Pi and Pj are disjoint. We show that for fixed k, this problem is solvable in polynomial time if the directed graph is planar. More generally, the problem is sol...

Splitting a graph into disjoint induced paths or cycles

A graph is an X-graph of Y-graphs (or two-level clustered graph) if its vertices can be partitioned into subsets (called clusters) such that each cluster induces a graph belonging to the given class Y and the graph of the clusters belongs to another given class X. Two-level clustered graphs are a useful and interesting concept in graph drawing. We consider the complexity of recognizing two-leve...

The Disjoint Paths Problem