Complete bipartite graph

Example

Let $m$ and $n$ be natural numbers. The complete bipartite graph $K_{m,n}$ is the graph whose vertex set is a disjoint union $A \sqcup B$ with $|A| = m$ and $|B| = n$. Two vertices are adjacent if and only if one is in $A$ and the other is in $B$.

Remarks

$K_{m,n}$ has $m + n$ vertices and $mn$ edges. It is bipartite with parts $A$ and $B$. For $m, n \ge 1$ its chromatic number is $2$. $K_{1,n}$ is a star. $K_{3,3}$ is not planar.

Explanations

L1 human

Split the vertices into two groups and join every vertex of one group to every vertex of the other group. There are no edges inside a group.