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











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












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






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








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















active

oldest

votes











Your Answer





StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");

StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});

function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});


}
});














 

draft saved


draft discarded


















StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2999230%2fwhat-is-the-lower-bound-of-number-of-degree-1-vertices-of-a-tree-with-no-degree%23new-answer', 'question_page');
}
);

Post as a guest















Required, but never shown






























active

oldest

votes













active

oldest

votes









active

oldest

votes






active

oldest

votes
















 

draft saved


draft discarded



















































 


draft saved


draft discarded














StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2999230%2fwhat-is-the-lower-bound-of-number-of-degree-1-vertices-of-a-tree-with-no-degree%23new-answer', 'question_page');
}
);

Post as a guest















Required, but never shown





















































Required, but never shown














Required, but never shown












Required, but never shown







Required, but never shown

































Required, but never shown














Required, but never shown












Required, but never shown







Required, but never shown







Popular posts from this blog

AnyDesk - Fatal Program Failure

How to calibrate 16:9 built-in touch-screen to a 4:3 resolution?

QoS: MAC-Priority for clients behind a repeater