NP-completeness of some edge-disjoint paths problems

The NP-Completeness of Some Edge-Partition Problems

We show that for each fixed n 3 it is NP-complete to determine whether an arbitrary graph can be edge-partitioned into subgraphs isomorphic to the complete graph Kn. The NP-completeness of a number of other edge-partition problems follows immediately.

The NP-completeness of some edge-partitioning problems

NP-completeness results for edge modification problems

The aim of edge modification problems is to change the edge set of a given graph as little as possible in order to satisfy a certain property. Edge modification problems in graphs have a lot of applications in different areas, and many polynomial-time algorithms and NP-completeness proofs for this kind of problems are known. In this work we prove new NP-completeness results for these problems i...

NP-Completeness and Disjoint NP-Pairs

We study the question of whether the class DisjNP of disjoint pairs (A,B) of NPsets contains a complete pair. The question relates to the question of whether optimal proof systems exist, and we relate it to the previously studied question of whether there exists a disjoint pair of NP-sets that is NP-hard. We show under reasonable hypotheses that nonsymmetric disjoint NP-pairs exist, which provi...

NP-Completeness of Some Tree-Clustering Problems

A graph is a tree of paths (cycles), if its vertex set can be partitioned into clusters, such that each cluster induces a simple path (cycle), and the clusters form a tree. Our main result states that the problem whether or not a given graph is a tree of paths (cycles) is NP-complete. Moreover, if the length of the paths (cycles) is bounded by a constant, the problem is in P.