All Questions
Tagged with order-theory graph-theory
12 questions with no upvoted or accepted answers
11
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0
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286
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Does every finite poset have a rigid endomorphism?
Crossposted on Mathematics.
In this post, an order-preserving self-map of a poset $X$ will be called an endomorphism of $X$, and such an endomorphism $f$ will be called rigid if the only automorphism ...
- 4,416
10
votes
0
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309
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Mapping graphs to ordinals
Robertson-Seymour theorem implies that graph minor relation is a well-quasi-ordering, which means (among other things) that this relation can be extended to a well-order, and other result says that ...
- 28.2k
6
votes
0
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188
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Generalized graph-minor theorem?
Consider the following generalized graph-minor theorem:
GM($κ,λ$): Given any collection $S$ of $κ$ simple undirected graphs each with less than $λ$ vertices, there are distinct graphs $G,H$ in $S$ ...
- 2,912
5
votes
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191
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Additional examples of classes of networks whose Hasse diagram of the poset is a perfect graph
This question is very important for my research, which is why I ask it here.
I do not have a formal background in graph theory so please excuse me if I state a term incorrectly (and feel free to ...
- 51
4
votes
0
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153
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Maximality with respect to having no marriage
Let $A,B\neq \emptyset$ be disjoint and suppose $G = (A\cup B, E)$ is bipartite where for all $e\in E$ we have $e\cap A \neq \emptyset\neq e\cap B$. For $a\in A$ we set $N_G(a) = \{b\in B: (\exists e\...
- 48.9k
3
votes
0
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127
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A class of Kripke frames which preserves validity
The background of our discussion is intuitionistic logic, i.e. the following definitions are intuitionistic Kripke frame.
For $1\leq s\leq n-2$, the frame $\mathcal{C}_n(s)$ denotes the frame which is ...
- 53
2
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0
answers
116
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Isomorphic subcategories of directed graphs and presets
For the purposes of this post, a digraph (directed graph) has neither loops nor multiple parallel edges, and a preset is an ordered pair consisting of a set $S$ and a preorder (viz., a reflexive and ...
- 10.5k
1
vote
0
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97
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Generalization of the linear extension theorem to directed acyclic graphs
Using Zorn's lemma one can prove a generalization of the order extension theorem, that states any acyclic digraph is always contained in another acyclic unilaterally connected digraph on the same ...
- 2,506
1
vote
0
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127
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Ordinal corresponding to well-quasi-order on graphs
Let $K$ be an infinite cardinal. Then, by the Robertson–Seymour theorem, the set of graphs with fewer than $K$ vertices and edges form a well-quasi-order.
In terms of $K$, what is the maximal order ...
- 6,353
1
vote
0
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111
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Set of upper bounds is finite for any finite subset
Is there a term to describe a preordered set $P$ in which any finite subset $S \subset P$ has at most finitely many minimal upper bounds? The preordered sets I'm studying generally aren't join-...
- 11
0
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115
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Quasi-transitive decomposition of a transitive graph
Let $G=(V,E)$ be a simple digraph that is semi-complete (ie. there's at least one arc between each unordered pair of vertices) and quasi-transitive (ie. its complement is transitive).
Is it true that ...
- 247
0
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0
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292
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Transitive closures and inductive reasoning [solved]
Let's say that r is an endorelation over A (i.e. $r$ is a subset of $A \times A$), $\bar{r}$ is the transitive closure of r (i.e. the least set containing r and being transitive).
Furthermore $r$ has ...
- 165