In Python, dataclass refers to a specific builtin library: https://docs.python.org/3/library/dataclasses.html

It can be confusing to mention it here.

I think this is supposed to say "the provided lists should not be modified" as lists are provided by-reference in Python and therefore can be accidentally changed.

Wasn't this done intentionally to ensure that MList returns MList?

I'm not entirely sure why this was based on producing an ordered list instead of a set either, I think maybe the author wasn't aware of sets in Python.

We know MList implements list, so:

test.expect(lst == list(mlisted))

will force it to use list.__eq__

The wording in this could maybe do with some rethinking. Instead of saying the sequence is graph-like, perhaps change the wording to something like:

Write a function which determines if the provided sequence of vertex degrees can be represented by a simple graph.

this introduces the idea of a simple graph up front instead of bringing it in later.

Now instead of going through the proxy of graph-like, we can directly explain what a simple graph is:

A simple graph is a graph without any loops (a vertex with an edge linking back to itself) and without multiple edges between any two vertices. A sequence of degrees can be represented by a simple graph if there exists any graph which satisfies these properties with the provided vertex degrees.

After front-loading that explanation we can then move on to demonstrating this:

The graph below represents a simple graph.

(2)-----(3)-----(3)-----(1)
 |       |       |
(2)     (2)      |
 |       |       |
 \------(3)------/

If you take the degrees from each vertex we end up with the sequence [2, 3, 3, 1, 2, 2, 3].

This second graph below however does not represent a simple graph, because it has a loop that folds back in on itself:

(2)--\
 |    |
  \--/

If we were to take all the degrees from each vertex (of which there is only one) in this graph, we would have the sequence [2].

So from these two graphs we can conclude that the sequence [2, 3, 3, 1, 2, 2, 3] can be represented as a simple graph so the function would return true, while the sequence [2] can not so the function would return false.

(However I've never written a Kata before so take this suggestion with a grain of salt)

1 = 0001
4 = 0100
5 = 0101

2 = 0010
5 = 0101
7 = 0111

3 = 0011
6 = 0110
7 = 0111