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Results tagged with graph-theory
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user 5903
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.
1
vote
Modification of Lemma 0 in Hajnal's paper "Embedding finite graphs into graphs colored with ...
A construction that uses the equality $\kappa^\lambda=\kappa$ directly runs as follows. By that equality the set $H$ has cardinality $\kappa$, so we can find a surjection $f:\kappa\to H$ such that for …
- 11.4k
3
votes
Accepted
Sieve for an infinite array of sets, resulting in an array of the same size of pairwise disj...
Consider the reverse lexicographic order $\prec$ on $\lambda\times\lambda^+$ ($(\alpha,\beta)\prec(\gamma,\delta)$ iff $\beta<\delta$ or $\beta=\delta$ and $\alpha<\gamma$); its order type is equal to …
- 11.4k
2
votes
Accepted
Large chromatic number in hypergraphs with large edges
For $\kappa=\aleph_0$ yes: there are (many) models with ultrafilters of character less than $\mathfrak{c}$. Let $E\subseteq[\omega]^\omega$ be a base for an ultrafilter, say $|E|=\aleph_1<\mathfrak{c} …
- 11.4k
2
votes
Accepted
Minimizing the set of "wrong" edges in $K_\omega$ with $\{0,1\}$-weights
I believe not: let $f$ be any colouring and take a maximal equivalence relation $\sim$ on $\omega$ with the property that $m\sim n$ implies $f(\{m,n\})=0$. Note that $\sim$ can be extreme: the identit …
- 11.4k
1
vote
Accepted
Compactness of Hadwiger number
Assume $K_n$ is a minor of $G$. Each vertex of $K_n$ corresponds to a connected subset of vertices of $G$ as it can only have been obtained by contracting edges. Each edge of $K_n$ can only have been …
- 11.4k