Hi and welcome to the Matladpi blog! In this post I will tell you the story of my tree generation and enumeration triplet.

It all started about five years ago. I saw a film, in which this genius solves a math problem. A graph theoretic one, to be precise. "Draw all homeomorphically irreducible trees of size n = 10."

The problem seemed new to me, as I had never done something like it before. But it happened almost instantly: I started to think trees as integer partitions. This is the idea that is my legacy; that number theory and graph theory are connected. That trees can be represented as integer (> 0) partitions, giving the opportunity to systematically generate and enumerate them with the three algorithms of mine.

The tree generation algorithm (TGA) took about four years to be completed. In 2015, the first versions of the condition matrix, vertex edge algebra and the algorithm were completed. At this stage the algorithm had only basic functionalities, as it could not generate free trees or homeomorphically irreducible trees either.

In 2017, after many rejections, I had made a somewhat more mathematical version of my tget. The enumeration algorithms branch form generator (BFG) and BFG->TGA had been added to the 2015 version, and the generation algorithm had a more systematic and rigorous structure. Also the condition matrix had more examples and possible parameters, and the rules for vertex edge algebra had been constructed.

It was not until in 2018 that I came up with the solution to the generation case for the free trees and the homeomorphically irreducible trees. Now the tget was getting quite ready! I did some blog posting of this tget later in that year, and published those posts right into the same blog you are currently reading.

The year 2019 was the final one for the tget. The idea had actually been completed about a year ago, but I made some improvements to the rules of vertex edge algebra and the structure of the tree generation algorithm. You can find this result as a book by searching Graph theory: Tree generation and enumeration triplet by Jesse Hyttinen. Njäf! said.

I am Jesse Sakari Hyttinen and I will see you in the next post!