We show that it is NP-complete to determine the chromatic index of an arbitrary graph. The problem remains NP-complete even for cubic graphs.

Many combinatorial problems are NP-complete for general graphs. However, when restricted to series–parallel graphs or partial k-trees, many of these problems can be solved in polynomial time, mostly in linear time. On the other hand, very few problems are known to be NP-complete for series–parallel graphs or partial k-trees. These include the subgraph isomorphism problem and the bandwidth probl...

Unknown relation between P and NP [3] complexity classes remains to be one of significant non solved problems in complexity theory. P complexity class consists of problems solvable by Deterministic Turing Machine (DTM) in polynomially bounded time, while NP complexity class consists of problem solvable by Non Deterministic Turing Machine (NDTM) in polynomially bounded time. This means that DTM ...

In this chapter, we will study the computational complexity of manipuation for three common voting rules. We will prove that the unweighted coalitional manipulation problem (Definition 3.1.2) is NP-complete for maximin (Section 4.1) and ranked pairs (Section 4.2), and we will give a polynomial-time algorithm for UCM for Bucklin (Section 4.3). 4.1 Manipulation for Maximin is NP-complete In this ...

We study the computational complexity of a packing puzzle Fillmat, which is a type of pencil-and-paper puzzles made by Japanese puzzle publisher Nikoli. We show that the problem to decide if a given instance of Fillmat has a solution is NP-complete by a reduction from the circuit-satisfiability problem (Circuit-SAT). Our reduction is carefully designed so that we can also prove ASP-completeness...

NP-complete problems are generally thought of as being com-putationally intractable. However, NP-completeness is a worst-case concept. Indeed, some NP-complete problems are \easy on average," though some may not be. How is one to know whether an NP-complete problem is \diicult on average"? The theory of average-case computational complexity , initiated by Levin about ten years ago, is devoted t...

Being NP complete has been widely interpreted as being computationally intractable But NP completeness is a worst case concept Some NP complete problems are easy on average but some may not be How is one to know whether an NP complete problem is di cult on average The theory of average case computational complexity initiated by Levin about ten years ago is devoted to studying this problem This ...

A matching-cut of a graph is an edge cut that matching. The problem recognizing graphs with and NP-complete, even if the belongs to one number classes. We initiate study for without fixed path as induced subgraph. show in P P5-free graphs, but there exists integer t>0 which it NP-complete Pt-free graphs.

task assignment problem (tap) involves assigning a number of tasks to a number of processors in distributed computing systems and its objective is to minimize the sum of the total execution and communication costs, subject to all of the resource constraints. tap is a combinatorial optimization problem and np-complete. this paper proposes a hybrid meta-heuristic algorithm for solving tap in a h...