# Combinatorics and Graph Theory

## 1608 Submissions

[2] **viXra:1608.0380 [pdf]**
*submitted on 2016-08-28 11:00:45*

### Tiling Hexagons with Smaller Hexagons and Unit Triangles

**Authors:** Richard J. Mathar

**Comments:** 10 pages are Java source code distributed under the LGPL 3.

This is a numerical study of the combinatorial problem of packing hexagons of some equal size
into a larger hexagon. The problem is well defined if all hexagon edges have integer length
and if their centers and vertices share the common lattice points of a triangular grid with unit distances.

**Category:** Combinatorics and Graph Theory

[1] **viXra:1608.0250 [pdf]**
*replaced on 2018-05-28 01:43:16*

### Hamiltonian Paths in Graphs

**Authors:** Atul Mehta

**Comments:** 7 Pages.

In this paper, we explore the connections between graphs and Turing
machines. A method to construct Turing machines from a general
undirected graph is provided. Determining whether a Hamiltonian
cycle exists is now shown to be equivalent to solving the halting
problem.
We investigate applications of the halting problem to problems in number theory.
A modified version of the classical Turing machine is now developed to
solve certain classes of computational problems.

**Category:** Combinatorics and Graph Theory