This is to be a highly pictorial encyclopaedia of graphs and orders which have significant applications.

The first installment is Part VIII of the freely available book at https://institute-theory-stem.org/combinatorics/ (or subsequent modifications of this, splitting it up into little webpages topic by topic). This concerns applying Combinatorics to itself. I.e. modelling the arenas – totalities of various kinds of Combinatorial objects can be done to some extent using graphs and orders: themselves branches of Combinatorics.

The next two installments shall cover graphs and orders arising in Flat Geometry. And graphs and orders arising in Theoretical Computer Science, in our “Arenize Knuth” (i.e. arenize everything in Knuth’s books) initiative. Expect the first few pieces of these installements to appear in 2025 -2026…

For now, here is an index of what is in the first installment.

And the first third of the first nontrivial Flat Geometry entry