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  "body": "\n## Statement\n\nLet $T$ be a [[tree|0MJ0JS72DZ]].\nThen $T$ is [[bipartite|07DVHJ8N0A]].\n\n## Remarks\n\nProof: fix a vertex $r$. Put a vertex in $A$ if its [[distance|0WPZ5YPAGR]] to $r$ is even, and in $B$ if it is odd. The ends of an edge have distances that differ by $1$.\nIt also follows from the theorem that [[a graph is bipartite iff it has no odd cycle|01R1HPEK6S]], because a tree has no cycle at all.\n\n## Explanations\n\n### L1 human\n\nColour the vertices of a tree by levels, from a chosen root: even levels white, odd levels black.\nEach edge goes between neighbouring levels, so it joins a white vertex and a black vertex.\n",
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