Let M be a real r × c matrix, and let k positive integer. In the column subset selection problem (CSSP), we need to minimize quantity ‖ − S A , where can an arbitrary runs over all submatrices of . This its applications in numerical linear algebra are being discussed for several decades, but algorithmic complexity remained open issue. We show that CSSP is NP-complete.

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...

We show that overloading is NP-complete. This solves exercise 6.25 in the 1986 version of the Dragon book.

Anti-Kekulé problem is a concept of chemical graph theory precluding the Kekulé structure of molecules. Matching preclusion and conditional matching preclusion were proposed as measures of robustness in the event of edge failure in interconnection networks. It is known that matching preclusion problem on bipartite graphs is NP-complete. In this paper, we mainly prove that anti-Kekulé problem on...