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