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Results tagged with extremal-graph-theory
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user 45255
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.
4
votes
Extremal examples for a folklore lemma on subgraphs of large minimum degree
Grids. (for one example only)
The grid $\overbrace{P_m \Box P_m \Box \cdots \Box P_m}^k$ has average degree about $2k$ as $m \rightarrow \infty$, but any subgraph seems to have to include a "corner" …
- 1,091
10
votes
1
answer
330
views
Can I weaken the minimum degree hypothesis in Nash-Williams' triangle decomposition conjecture?
In what follows, all graphs $G$ are $K_3$-divisible (all degrees even, number of edges a multiple of three) on $n$ vertices, where $n$ is not too small.
The famous Nash-Williams conjecture claims tha …
- 1,091
4
votes
Are all almost regular graphs obvious?
Here are a few more observations.
(1) Recall a consequence of Dirac's Theorem: A simple graph $G$ on $2n$ vertices admits a one-factor if $\delta(G) \ge n$. (This is a sufficient, but not necessary …
- 1,091