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Results tagged with extremal-graph-theory
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user 40335
Study of graphs satisfying a property that are maximal or minimal with respect to some parameter. A classic example is Turán's Theorem, which exactly characterizes the densest graphs on $n$ vertices without a $K_t$ subgraph.
1
vote
Accepted
The edit distance from a large complete $p$-partite graph to the Turán graph
For the first inequality:
\begin{align*}
\sum(|V_i| -\frac{n}{p})^2 &= \sum\left(|V_i|^2 - 2\frac np |V_i| + \frac{n^2}{p^2}\right) \\
&= \left(\sum |V_i|^2\right) - 2n^2/p + n^2/p \\
&= 2\left( \sum …
- 242
3
votes
Quasi-random vs pseudo-random graphs
Someone else will probably have a better answer, but I can't leave a comment. In my experience "quasi-random graph" (almost?) always refers to the Chung Graham Wilson type graphs you referred to.
"pse …
- 242
2
votes
Accepted
Covering a bounded degree graph with subgraphs of bounded sizes
I think there is a simple solution to this.
Let $r$ be sufficiently large and partition $V(G)$ (approximately) evenly into sets $V_1, V_2, \ldots, V_{n/r}$. Your $G_i$s will be the graphs induced on t …
- 242