Algorithmes Quantiques, Cycles Hamiltoniens et la k-coloration des Graphes

Mohamed Sghiar (1)

1 Chercheur indépendant

I will prove the existence of the Feynman quantum algorithm, polynomial and of the order $ \mathcal{ O } (n ^ 3 ) $ which inform us about the presence of the Hamiltonian cycles in a graph with cardinality n and in this case allows us to find them completely. And I will also prove the existence of the Pauli quantum algorithm with the order $\mathcal { O } (n ^ 3) $ which enable us to know whether the k-coloring graph is possible and make us this coloration if it is possible.

Mots clés: Algorithme; k-coloration des graphes; voyageur de commerce; P=NP; cycle hamiltonien; Graph; hamiltonien; Algorithme quantique; Théorie de la complexité

Domaines: Combinatoire [math.CO]; Théorie de l'information et codage [math.IT]; Logique [math.LO]; Intelligence artificielle [cs.AI]; Complexité [cs.CC]; Informatique et langage [cs.CL]; Cryptographie et sécurité [cs.CR]; Mathématique discrète [cs.DM]; Informatique et théorie des jeux [cs.GT]

Mohamed Sghiar. Algorithmes Quantiques, Cycles Hamiltoniens et la k-coloration des Graphes. Pioneer journal of mathematics and mathematical sciences, 2016, 17 (1). ⟨hal-01288408⟩