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Results tagged with graph-theory
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user 99278
Questions about the branch of combinatorics called graph theory (not to be used for questions concerning the graph of a function). This tag can be further specialized via using it in combination with more specialized tags such as extremal-graph-theory, spectral-graph-theory, algebraic-graph-theory, topological-graph-theory, random-graphs, graph-colorings and several others.
3
votes
Accepted
Name and information about this graph
In the case of simple graphs, you could search the House of Graphs (http://hog.grinvin.org) or browse the Information System on Graph Classes and their Inclusions (http://www.graphclasses.org).
Beca …
- 399
2
votes
Components of bipartite graphs that are trees
Clinton Conley, Jul 13 '11 at 22:19 answered:
A finite forest has strictly fewer edges than vertices. And a finite graph with no acyclic connected component has at least as many edges as vertices. …
- 399
4
votes
1
answer
1k
views
What is the minimum diameter of $r$-regular, $k$-connected graphs?
Let $md_r^k(n)$ be the minimum diameter over all $r$-regular, $k$-connected graphs on at least $n$ vertices. (Let us assume $r, k \geq 2$).
Problem: Find lower and upper asymptotic bounds on $md_r …
- 1,687
1
vote
A traveling time problem
Lemma 1: Suppose a city has $d$ incident links, the least-used one(s) having been used $m$ times. Then the city has been visited at
most $d(m+1)$ times.
Proof: Every visit to a city increases t …
- 399
6
votes
0
answers
108
views
Localizing Bondy's metaconjecture on hamiltonicity
Definitions:
Let $G$ be a graph on $n$ vertices. $G$ is Hamiltonian provided $G$ has a cycle of length $n$. $G$ is pancyclic provided $G$ has a cycle of length $\ell$ for every $3 \leq \ell \leq n$.
…
- 399
1
vote
Ratio between number of nodes and leaves in a rooted binary tree
We can prove a lower bound on the expression by considering only vertices immediately below a leaf:
$$\frac{[\sum_{v \in T \text{ not a leaf}}2^{h(v)}L(T(v))] + L(T)}{N(T)} \geq \frac{[\sum_{v \text{ …
- 399