We were asked to suggest a dynamic program algorithm to Find maximum matching in a tree in linear time, $O(|V|+|E|)$.
I have no clue how to start. any Ideas?
2026-03-26 04:49:42.1774500582
Maximum matching in a tree
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Hint:
Denote by $A(v,\text{True})$ the maximal matching in the sub-tree where $v$ is its root, where edges with one endpoint equal to $v$ are allowed.
Denote by $A(v,\text{False})$ the maximal matching in the sub-tree where $v$ is its root, where edges with one endpoint equal to $v$ are not allowed.
Feel free to ask for some clarifications if this does not help you :)