Related papers: The Quiver Problem is NP Complete
We prove Union-Closed sets conjecture.
Boolean satisfiability problem has applications in various fields. An efficient algorithm to solve satisfiability problem can be used to solve many other problems efficiently. The input of satisfiability problem is a finite set of clauses.…
We prove some symmetric $q$-congruences.
The Navier-Stokes (NS) problem consists of finding a vector-function $v$ from the Navier-Stokes equations. The solution $v$ to NS problem is defined in this paper as the solution to an integral equation. The kernel $G$ of this equation…
All the finite order entire solutions of \begin{equation*} f^n(z)+q(z)e^{Q(z)}f^{(k)}(z+c)=P(z) \end{equation*} are given, where $ q(z) $, $ Q(z), P(z) $ are polynomials, $ k $ and $ n \geq 2 $ are integers, and $ c \in \mathbb{C} \setminus…
In this paper, we prove the conjecture that if there is an odd perfect number, then there are infinitely many of them.
We show that the problem of finding a set with maximum cohesion in an undirected network is NP-hard.
In this paper, we prove that the Fechner and Stevens laws are equivalent (coincide up to isomorphism). Therefore, the problem does not exist.
Given a graph $G$ with a total order defined on its vertices, the Maximum Pagenumber-$k$ Subgraph Problem asks for a maximum subgraph $G'$ of $G$ such that $G'$ can be embedded into a $k$-book when the vertices are placed on the spine…
An algebraic proof is presented for the finite strong standard completeness of involutive uninorm logic with fixed point. The result may provide a first step towards settling the open standard completeness problem for involutive uninorm…
We study the satisfiability problem for a modal logic expressing knowing-how assertions, which captures an agent's ability to achieve a given goal under the standard semantics based on linear plans. Our main result shows that satisfiability…
In [BNRR], it was shown that tiling of general regions with two rectangles is NP-complete, except for a few trivial special cases. In a different direction, R\'emila showed that for simply connected regions by two rectangles, the…
We prove that every countable group with solvable power problem embeds into a finitely presented 2-generated group with solvable power and conjugacy problems.
In this paper, we prove that the MaxCut problem is NP-complete on permutation graphs, settling a long-standing open problem that appeared in the 1985 column of the "Ongoing Guide to NP-completeness" by David S. Johnson.
This paper investigates an extremely classic NP-complete problem: How to determine if a graph G, where each vertex has a degree of at most 4, can be 3-colorable(The research in this paper focuses on graphs G that satisfy the condition where…
We study the stable matching problem in non-bipartite graphs with incomplete but strict preference lists, where the edges have weights and the goal is to compute a stable matching of minimum or maximum weight. This problem is known to be…
It is well known that the resolution method (for propositional logic) is complete. However, completeness proofs found in the literature use an argument by contradiction showing that if a set of clauses is unsatisfiable, then it must have a…
The nonnegative inverse eigenvalue problem (NIEP) is shown to be solvable by the reality condition, spectrum equal to its conjugate, as well as by a finite union and intersection of polynomial inequalities. It is also shown that the…
We consider the problem of covering hypersphere by a set of spherical hypercaps. This sort of problem has numerous practical applications such as error correcting codes and reverse k-nearest neighbor problem. Using the reduction of non…
In this paper we define a restricted version of Monotone NAE-3SAT and show that it remains NP-Complete even under that restriction. We expect this result would be useful in proving NP-Completeness results for problems on $k$-colourable…