Search Results

Finite graphs which are homomogeneous, that is, every isomorphism between induced subgraphs extends to an automorphism, are extremely special and have been classified. Indeed, even the graphs which a …

Let $X$ be an infinite set, and let $G$ be the symmetric group on $X$. I want to understand $G$ by putting a topology on it, without imposing any more structure on $X$. What 'interesting' possibilit …

Having thought about it some more, there ought to be an abundance of examples here. This is not quite an answer as I haven't thought of an explicit example yet, but hopefully I am getting close to un …

If I've understood the hypotheses correctly, the covering relation gives a connected locally finite directed graph: starting from a point $x$, the maximal elements underneath it form a finite antichai …

Let $G$ and $H$ be permutation groups on the natural numbers such that the orbits of $G$ and $H$ are all finite. Suppose that for all $\pi \in Sym(\mathbb{N})$, there is some $N$ (depending on $\pi$) …

Let $M$ be a meet-semilattice with a least element $0$. Suppose there is an order-reversing involution $a \mapsto -a$ on $M$ such that for all $a, b \in M$, $a \wedge b = 0$ if and only if $b \le -a$ …

The Rado graph (or countable random graph) is graph theory's answer to the normal distribution. It seems almost any sensible definition of drawing edges on a countable graph 'randomly' or even 'pseud …