What is the lower bound of number of degree 1 vertices of a tree with no degree 2 vertices?











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Here is the question:




Let $G$ be a tree with $n$ vertices, and no vertex in the tree has degree $2$. Find a function of $n$ that indicates the lower bound of the number of degree $1$ vertices in the tree.




with handshake lemma and Euler's formula, I get $n_1 =2 + sum_{k =3}^{infty} (k-2)n_k$ where $n_k$ is the number of degree $k$ vertices. However, this result cannot tell me the lower bound of $n_1$.



I guess the result is $n -biglfloor frac{n}{2} bigrfloor$, but not sure how to prove this.



Please give me some hint, thank you.










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  • math.stackexchange.com/questions/1484941/…
    – Alexander Gruber
    Nov 15 at 4:59















up vote
1
down vote

favorite












Here is the question:




Let $G$ be a tree with $n$ vertices, and no vertex in the tree has degree $2$. Find a function of $n$ that indicates the lower bound of the number of degree $1$ vertices in the tree.




with handshake lemma and Euler's formula, I get $n_1 =2 + sum_{k =3}^{infty} (k-2)n_k$ where $n_k$ is the number of degree $k$ vertices. However, this result cannot tell me the lower bound of $n_1$.



I guess the result is $n -biglfloor frac{n}{2} bigrfloor$, but not sure how to prove this.



Please give me some hint, thank you.










share|cite|improve this question
























  • math.stackexchange.com/questions/1484941/…
    – Alexander Gruber
    Nov 15 at 4:59













up vote
1
down vote

favorite









up vote
1
down vote

favorite











Here is the question:




Let $G$ be a tree with $n$ vertices, and no vertex in the tree has degree $2$. Find a function of $n$ that indicates the lower bound of the number of degree $1$ vertices in the tree.




with handshake lemma and Euler's formula, I get $n_1 =2 + sum_{k =3}^{infty} (k-2)n_k$ where $n_k$ is the number of degree $k$ vertices. However, this result cannot tell me the lower bound of $n_1$.



I guess the result is $n -biglfloor frac{n}{2} bigrfloor$, but not sure how to prove this.



Please give me some hint, thank you.










share|cite|improve this question















Here is the question:




Let $G$ be a tree with $n$ vertices, and no vertex in the tree has degree $2$. Find a function of $n$ that indicates the lower bound of the number of degree $1$ vertices in the tree.




with handshake lemma and Euler's formula, I get $n_1 =2 + sum_{k =3}^{infty} (k-2)n_k$ where $n_k$ is the number of degree $k$ vertices. However, this result cannot tell me the lower bound of $n_1$.



I guess the result is $n -biglfloor frac{n}{2} bigrfloor$, but not sure how to prove this.



Please give me some hint, thank you.







graph-theory trees






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edited Nov 15 at 5:01









Alexander Gruber

20.1k24102171




20.1k24102171










asked Nov 15 at 4:53









Enllwx

112




112












  • math.stackexchange.com/questions/1484941/…
    – Alexander Gruber
    Nov 15 at 4:59


















  • math.stackexchange.com/questions/1484941/…
    – Alexander Gruber
    Nov 15 at 4:59
















math.stackexchange.com/questions/1484941/…
– Alexander Gruber
Nov 15 at 4:59




math.stackexchange.com/questions/1484941/…
– Alexander Gruber
Nov 15 at 4:59















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