Use this tag for questions in graph theory. Here a graph is a collection of vertices and connecting edges. Use (graphing-functions) instead if your question is about graphing or plotting functions.

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5
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Restriction of a monotone self-map (“endomorphism of $\mathbf{Pos}$”) to a wide subposet

Here's a poset, call it $P.$ $\hspace{1cm}$ Define a function $S : P \rightarrow P$ as follows. $$S(0) = 1, \qquad S(1) = 2, \qquad S(2) = 2$$ Clearly, $S$ is monotone. Now consider the following ...
4
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The graph has an Euler tour iff in-degree($v$)=out-degree($v$)

I am looking at the proof that $G$ has an Euler tour iff in-degree($v$)=out-degree($v$), that I found at this site: www.cs.duke.edu/courses/fall09/cps230/hws/hw3/headsol.pdf (Problem 2) A simple ...