The NP-Completeness of Some Edge-Partition Problems

Some NP-complete edge packing and partitioning problems in planar graphs

Graph packing and partitioning problems have been studied in many contexts, including from the algorithmic complexity perspective. Consider the packing problem of determining whether a graph contains a spanning tree and a cycle that do not share edges. Bernáth and Király proved that this decision problem is NP-complete and asked if the same result holds when restricting to planar graphs. Simila...

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...

The NP-completeness of some edge-partitioning problems

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...

Molecular Computing Solutions of some Classical Problems

In this paper we give efficient molecular computing solutions to seven well-known NP-complete problems, namely the Hamiltonian circuit, Path with forbidden pairs, Longest path, Monochromatic triangle, Partition into triangles, Partition into paths of length two, Circuit satisfiability problems in the Parallel filtering model of Amos et al.