How to interpret a limit in a graph theory result
up vote
1
down vote
favorite
The following is a theorem in the linked paper here.
To add some context, the authors also state:
Throughout this paper...$t^k$, the average degree, will always be an increasing function of $n$, the number of vertices of the hypergraph, i.e., $t = t(n) to infty$ with $n to infty$
How does one interpret the limit in the above sentence? Currently I am interpreting it as: if you add more and more vertices to your hypergraph, the $k$-th root of the average degree should also increase, but that doesn't seem to make much sense. I suppose my main trouble here is: are there particular $(k+1)$-uniform hypergraphs to which Theorem 2.4 cannot be applied, owing to the aforementioned limit?
graph-theory extremal-graph-theory
asked 2 days ago
David Smith
305210
add a comment |
up vote
1
down vote
favorite
The following is a theorem in the linked paper here.
To add some context, the authors also state:
Throughout this paper...$t^k$, the average degree, will always be an increasing function of $n$, the number of vertices of the hypergraph, i.e., $t = t(n) to infty$ with $n to infty$
How does one interpret the limit in the above sentence? Currently I am interpreting it as: if you add more and more vertices to your hypergraph, the $k$-th root of the average degree should also increase, but that doesn't seem to make much sense. I suppose my main trouble here is: are there particular $(k+1)$-uniform hypergraphs to which Theorem 2.4 cannot be applied, owing to the aforementioned limit?
graph-theory extremal-graph-theory
asked 2 days ago
David Smith
305210
I wasn't sure if I provided enough context. I will post the entire theorem in question.
– David Smith
2 days ago
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
The following is a theorem in the linked paper here.
To add some context, the authors also state:
Throughout this paper...$t^k$, the average degree, will always be an increasing function of $n$, the number of vertices of the hypergraph, i.e., $t = t(n) to infty$ with $n to infty$
How does one interpret the limit in the above sentence? Currently I am interpreting it as: if you add more and more vertices to your hypergraph, the $k$-th root of the average degree should also increase, but that doesn't seem to make much sense. I suppose my main trouble here is: are there particular $(k+1)$-uniform hypergraphs to which Theorem 2.4 cannot be applied, owing to the aforementioned limit?
graph-theory extremal-graph-theory
asked 2 days ago
David Smith
305210
The following is a theorem in the linked paper here.
To add some context, the authors also state:
Throughout this paper...$t^k$, the average degree, will always be an increasing function of $n$, the number of vertices of the hypergraph, i.e., $t = t(n) to infty$ with $n to infty$
How does one interpret the limit in the above sentence? Currently I am interpreting it as: if you add more and more vertices to your hypergraph, the $k$-th root of the average degree should also increase, but that doesn't seem to make much sense. I suppose my main trouble here is: are there particular $(k+1)$-uniform hypergraphs to which Theorem 2.4 cannot be applied, owing to the aforementioned limit?
graph-theory extremal-graph-theory
graph-theory extremal-graph-theory
asked 2 days ago
David Smith
305210
asked 2 days ago
David Smith
305210
edited 2 days ago
asked 2 days ago
David Smith
305210
asked 2 days ago
David Smith
305210
asked 2 days ago
David Smith
305210
305210
I wasn't sure if I provided enough context. I will post the entire theorem in question.
– David Smith
2 days ago
add a comment |
I wasn't sure if I provided enough context. I will post the entire theorem in question.
– David Smith
2 days ago
I wasn't sure if I provided enough context. I will post the entire theorem in question.
– David Smith
2 days ago
I wasn't sure if I provided enough context. I will post the entire theorem in question.
– David Smith
2 days ago
add a comment |
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2996514%2fhow-to-interpret-a-limit-in-a-graph-theory-result%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
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
I wasn't sure if I provided enough context. I will post the entire theorem in question.
– David Smith
2 days ago