# Tagged Questions

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### Why can disjoint subsets be picked out in these sets?

Still another exercise on Reinhard Diestel Graph Theory, GTM 173, edition 3 (on page 51) Let $A$ be a finite set with subsets $A_1, \cdots, A_n$, and let $d_1, \cdots, d_n \in \mathbb N$. Show ...
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### Confusion about the definition of graphs

From this graph theory lesson : A graph is a non-empty finite set $V$ of elements called vertices together with a possibly empty set $E$ of pairs of vertices called edges. Here are a few ...
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### Minimum size of a subset to know a complete total order

Lets say we have a set $A$. Suppose that $A$ is ordered by $<$, $A$ is completely ordered. $<$ can be defined as $<:=\{(a,b) \in A\times A : a<b \}$ Given that $<$ is transitive, it ...
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### Is the Set of all Graphs Countable?

I am taking an elementary level set theory, and was doing an exercise. The question is "Is the set of all graphs countable?" My intuition tells me it is not but I am not sure how I can use Cantor's ...
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### directed graph representing the inverse relation

Let $R$ be a relation on a set $A$. Explain how to use the directed graph representing $R$ to obtain the directed graph representing the inverse relation $R^{-1}$ ($R$ inverse).
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### Cardinality of the set of graphs on a infinite set of vertices

How might one label an infinite graph (which edges can cross over and all nodes are connected to at least 2 edges, such that there are no "dangling lines") to show that there are countably many such ...
I'm sorry if the title is a bit convoluted. I'm a bit unsure how to formulate this condition in words, see below instead. Say we are given a set $Y$. I want to find the following set: $\mathcal{A}$ ...