Alternative words for "parts" of a bi-partite graph Perhaps the most common term for each of the two disjoint sets in a bipartite graph is "part". So I can say for example:

One "part" of the $K_{4,4}$ connects to a corresponding "part" of a
  different graph while the other "part" does
  not.

What are the synonyms (if any) that could be appropriate for replacing the word "part" here?
I am writing a paper for a very non-mathematical audience. This small community of researchers have come to learn what $K_{4,4}$ means, because it comes up often, but they have no other graph theory training and it will not be clear to them what "part" means. For example, the English word "part" could describe things like individual "vertices" or "edges". If the reader thinks long enough about the above example sentence, eventually they will probably figure out that we are talking about the two disjoint sets of the graph. However, to make things less confusing I would like to avoid a word like "part" which can mean so many different things in the English language.
We could use "disjoint sets" but the words "disjoint" and "set" won't be immediately familiar with the readers. 
My current preferred term would be "partition" because when a country is partitioned, the average English speaker knows that "partition A" and "partition B" are the two disjoint partitions formed by the partitioning. However, for the very few people reading the paper that are trained in graph theory for example, would my use of the word "partition" be in-appropriate? 
If so, what would be the alternatives to the word "part" that I can use? 
 A: "Part" works reasonably well, but "partite set" is also common and is more specific. For example, "in a regular bipartite graph the two parts are the same size" is relatively clear, but "in a regular bipartite graph the two partite sets are the same size" is unambiguous.
You can also use "partite set" to refer to the same notion in $k$-partite graphs.
When defining a bipartite graph, it is nice to say "Let $G$ be a bipartite graph with bipartition $(A,B)$" and then you can refer to the two parts as $A$ and $B$. In general, "bipartition" is a good word to disambiguate with: if you're talking about a bipartite graph $G$ and worried that "both parts of $G$ contain four vertices" is ambiguous, then "both parts of the bipartition of $G$" clarifies things.
Instead of talking about the two parts of the bipartition, you can talk about the two "sides" of the bipartition. For example, "When vertices $u$ and $v$ are on the same side of the bipartition, there is no edge between them." This may be a good choice if you're dealing with a non-mathematical audience, because "side" has an intuitive meaning.
Using "partition" to refer to either $A$ or $B$ would not be correct. A partition refers to the whole structure of a set written as the union of several disjoint subsets. Whenever you write any set $S$ as $S = A \cup B$ with $A \cap B = \varnothing$, you can call $A$ and $B$ the "parts" of this partition, but they are not individually "partitions".
