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Results tagged with graph-theory
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user 45255
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.
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
4
votes
1
answer
70
views
Balancing out edge multiplicites in a graph
Let $G$ be a multigraph with maximum edge multiplicity $t$ and minimum edge multiplicity $1$ (so that there is at least one 'ordinary' edge).
Is there some simple graph $H$ such that the $t$-fold mul …
- 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
2
votes
Is the domination number of a combinatorial design determined by the design parameters?
Gordon has done a proper search of $(15,3,1)$-designs. I guess my incorrect reasoning does lead to a computer-free proof for (15,3,13)-designs. This is kind of cheating though, because there are rep …
- 1,091
4
votes
Linear algebra proofs in combinatorics?
Variants of the EKR Theorem offer a wide class of examples. This page has a nice list going, by the way.
A friend of mine once made the outrageous claim -- but hear me out -- that most "linear algeb …
5
votes
Accepted
Could a perfect squared square be split into two perfect squared squares?
Nice question. This is not (any longer) an answer, but a strategy.
First, try to construct 25 mutually disjoint squared squares of the same order. Then arrange them according to a 3,4,5 template.
…
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