All Questions
4 questions
10
votes
1
answer
492
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is there a ‘nice’ lattice on the set of unlabelled graphs with $n$ vertices?
It is easy to endow the set of vertex-labelled graphs with $n$ vertices with a lattice structure: take the union and the intersection of the edge set as meet and join respectively.
However, I wonder ...
- 5,822
4
votes
1
answer
503
views
For what classes of comparability graphs are their complements also comparability graphs?
An interval graph is an intersection graph of real intervals, that is, an undirected graph whose vertices can be labeled with real intervals so that there is an edge between two vertices iff their ...
- 43
3
votes
2
answers
138
views
In the context of directed graphs is it standard notation to allow an element of an independent vertex set to be contained in a loop?
Given any relation $R$, that is, any set of ordered pairs, we can associate a unique digraph $D$ to our relation $R$ by setting $D=(\text{fld}(R),R)$ where $\text{fld}(R)=\text{dom}(R)\cup\text{rng}(R)...
- 2,506
2
votes
0
answers
116
views
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