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  "body": "\n## Definition\n\nLet $G$ be a [[graph|0JD5C82QMB]] with vertex set $V$.\nThen $G$ is bipartite if $V$ is the union of two disjoint sets $A$ and $B$ with this property.\nEach edge of $G$ has one end in $A$ and one end in $B$.\nThe pair $(A, B)$ is a bipartition of $G$.\n\n## Remarks\n\nEquivalently, $G$ is bipartite if it has a proper [[colouring|0874138YP6]] with $2$ colours.\nThe [[complete bipartite graphs|0V0GC7BQAN]], the even [[cycle graphs|0QQ0F12962]] and all [[trees|0MJ0JS72DZ]] are bipartite.\nA graph is bipartite if and only if it has no cycle of odd length. The node [[a graph is bipartite iff it has no odd cycle|01R1HPEK6S]] states this.\n\n## Explanations\n\n### L1 human\n\nA graph is bipartite when its vertices split into two groups, and every edge goes between the groups.\nStudents and the courses they take form a bipartite graph.\n",
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