[2] **viXra:1806.0225 [pdf]**
*submitted on 2018-06-19 06:33:05*

**Authors:** Robert DiGregorio

**Comments:** 2 Pages.

A problem exists that’s hard to solve but easy to verify a solution for.

**Category:** Data Structures and Algorithms

[1] **viXra:1806.0145 [pdf]**
*replaced on 2018-06-17 03:01:49*

**Authors:** Óscar Emilio Chamizo Sánchez

**Comments:** 6 Pages. Minor errors corrected in algorithmic design.

Hamiltonian circuit problem (HCP for short) is one of the most famous and deeply
investigated problem in computation. Given a (directed or undirected, 2 or 3 dimensional1)
graph the simple goal is to answer to the question whether exists or not a circuit that visits each vertex exactly once. Since the problem of finding a Hamiltonian circuit is NP-complete, the only known way so far to find whether a general graph has a Hamiltonian circuit was to perform and exhaustive search with exponential execution time. In this paper we present an interesting supplement from our paper: "A new approach: A hardware device model solving Traveling Salesman Problem in O(n2) time. Practical application and theoretical consequences" [1] now solving any instance of HCP in O(n2) time. In section 1 we go directly to the device model and prove mathematically its validity. In section 2 we explain the basic ideas behind the model. In section 3 we analyze complexity and software and hardware design.

**Category:** Data Structures and Algorithms