Generator
complete-graph
A generator in the discrete library, called 5 times across 1 essays. Below: what it draws at its defaults and at each mode an essay asks for, what it checks while drawing, and everywhere it is used.
complete-graph is one function. Everything below came out of it during this
build, at parameters taken from the essays rather than invented for this page — so a figure
here is the same figure a reader meets in an essay, and if the generator changes, this page
changes with it.
At its defaults
show: "vertex"
show: "five"
What it checks while it draws
Collected by running the family and listening to lib/verify.js, not written
here. The count is how many separate times this build put that claim to the test.
- a vertex meets five others ×1
- and in fact at least two, which is Goodman's bound ×1
- EVERY colouring of six people contains a monochromatic triangle ×1
- five edges in the pentagon ×1
- K5 has ten edges ×1
- K6 has fifteen edges ×1
- no triangle has all three edges the same colour ×1
- the three ends make three pairs, and any one of them closes a trio ×1
- this colouring has a monochromatic triangle ×1
- two colours over five edges forces three of one ×1
Where it is called
Changing this generator changes every figure on this list. That is what makes the list worth publishing rather than keeping in a check script.