A Graph Theoretical Approach to the Collatz Problem release_fnm3ow4pjvhzjblnbiwsfihqna

by Heinz Ebert

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2020  

Abstract

Andrei et al. have shown in 2000 that the graph C of the Collatz function starting with root 8 after the initial loop is an infinite binary tree A(8). According to their result they gave a reformulated version of the Collatz conjecture: the vertex set V(A(8))=ℤ^+. In this paper an inverse Collatz function C with eliminated initial loop is used as generating function of a Collatz graph C_C. This graph can be considered as the union of one forest that stems from sequences of powers of 2 with odd start values and a second forest that is based on branch values y=6k+4 where two Collatz sequences meet. A proof that the graph C_C(1) is an infinite binary tree A_C with vertex set V(A_C(1))=ℤ^+ completes the paper.
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Date   2020-11-11
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arXiv  1905.07575v3
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