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Results tagged with co.combinatorics
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user 158328
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
4
votes
Accepted
Random graphs defined by a set of tiles
The question you ask is, in my opinion, extremely important: decomposing a graph into a (small) set of small graphs (the tiles or ego-centered sub-graphs, for instance), and then characterizing how th …
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7
votes
Is there a term for a subgraph which includes all the edges of a graph?
If the subgraph includes all edges of the original graph, then it also includes all its vertices, except maybe some with degree $0$.
The minimal such subgraph is the graph in which all $0$-degree vert …
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4
votes
Smallest $3$-regular graph with a unique perfect matching
Regarding your second even better question, I warmly suggest the Brendan McKay page on combinatorial objects, that gives many kinds of graph examples.
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3
votes
Finding a subclass of lattices in the literature
I suggest the following directions, although I am not sure they may help in your specific case.
As you have a list for each $n$, you may consider the sequence defined by their length, and query The O …
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1
vote
Degree sequences after vertex removals
Several works study the degree sequence obtained when vertices are removed from random graphs with given degree sequence. Vertices are generally removed by decreasing order of degrees, or uniformly at …
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8
votes
Rhombus tilings with more than three directions
This post is almost ten years old, but I find it interesting and I would like to add a few pointers from my PhD, itself about 20 years old.
First, in the paper Integer Partitions, Tilings of 2D-gons a …
2
votes
0
answers
135
views
Writing integers as sequences of products by 2 and integer divisions by 3
For any integer, we consider its decompositions into sequences of products by $2$ and integer division by $3$.
For instance:
$$
100 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 …
- 1,444
2
votes
What nodes of a graph should be vaccinated first?
This is a much studied question, at the crossroad of several fields: epidemiology, mathematics, statistical mechanics, and computer science, at least.
The model you consider is known as SI with parame …
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2
votes
Random subgraph properties
I fear the question is difficult in its general form: the answer will strongly depends on the assumptions we make regarding the initial graph, and on how we choose $n$.
As noticed by @dodd, in particu …
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2
votes
is there a ‘nice’ lattice on the set of unlabelled graphs with $n$ vertices?
I guess this class is way too small, but since the questions is still unanswered, I will give you an example I like.
An EFG (Edge Firing Game) is defined from an undirected graph $G$ with a distinguis …
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10
votes
Lattices on classical combinatorial families
Lattices are prevalent when one deals with integer partitions.
Let me give a few examples with pictures, that I hope you will enjoy despite the poor quality due to bitmap conversion.
The dominance ord …
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