NP-completeness of some problems of partitioning and covering in graphs

The NP-completeness of some edge-partitioning problems

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.

NP-completeness and FPT Results for Rectilinear Covering Problems

This paper discusses three rectilinear (that is, axis-parallel) covering problems in d dimensions and their variants. The first problem is the Rectilinear Line Cover where the inputs are n points in R and a positive integer k, and we are asked to answer if we can cover these n points with at most k lines where these lines are restricted to be axis parallel. We show that this problem has efficie...

NP-completeness results for some problems on subclasses of bipartite and chordal graphs

Extending previous NP-completeness results for the harmonious coloring problem and the pair-complete coloring problem on trees, bipartite graphs and cographs, we prove that these problems are also NP-complete on connected bipartite permutation graphs. We also study the k-path partition problem and, motivated by a recent work of Steiner [G. Steiner, On the k-path partition of graphs, Theoret. Co...

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.