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Tagged with matching-theory trees
7
questions
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Problem in proving that every tree has at most one perfect matching.
I would like to prove that every tree has at most one perfect matching. I approached it in the same way as described here: Perfect matching in a tree. However, I don't understand the concluding ...
user1316790
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Let $G$ a tree, $M$ maximum matching of $G$, then some leaf (vertex of degree 1) of $G$ is $M-$saturated.
Let $G$ a tree, $M$ maximum matching of $G$, then some leaf (vertex of degree 1) of $G$ is $M-$saturated.
I am trying to do this problem by contradiction. Thus, since there are no M-saturated leaves, ...
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Not more than one perfect matching in a tree
I have to show that a tree $T = (V,E)$ has at most one perfect matching.
In order to show that, one has to assume that the tree $T$ has an even number of vertices, so that a perfect matching can exist....
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2
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Matchings in a tree
Let $T$ be a tree.
Suppose that $T$ doesn’t have a perfect matching and let $M$ be a matching of $T$, $|M| = k$. Prove
that there exists a matching of the same cardinality $k$ which exposes at least a ...
user866415
1
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1
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Perfect matchings and parity of the vertices and the edges in a tree
So I'm trying to solve a problem in graph theory.
I painted a couple of trees with perfect matchings and a couple of graphs without perfect matchings.
And I have realized that when I paint non perfect ...
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2
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A tree has at most one perfect matching (proof verification)
Question: Let $T$ be a tree, prove that at most $1$ perfect matching exists in $T$
My Proof:
Let $M$ and $M'$ be perfect matches in the tree $T = (V,E)$
And let $G$ be a graph on the vertex set $V$ ...
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Perfect matching in a tree
Prove that in a tree there is at most $1$ perfect matching
If the number of vertices is even$\implies$ number of edges odd, not divisible by $2$, so no perfect matching
For the other case can you ...
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