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Results tagged with graph-theory
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user 5010
Questions about the branch of combinatorics called graph theory (not to be used for questions concerning the graph of a function). This tag can be further specialized via using it in combination with more specialized tags such as extremal-graph-theory, spectral-graph-theory, algebraic-graph-theory, topological-graph-theory, random-graphs, graph-colorings and several others.
3
votes
Connectedness of the complements of the connected subsets
(B) does not hold for topological graphs. Let $X$ be the 1-skeleton of a tetrahedron, and let $S$ be a cycle of 4 edges. Then $X \setminus S$ is not connected.
- 10.1k
12
votes
0
answers
261
views
Computing the number of ways to delete vertices sequentially without disconnecting a graph
Given a finite connected graph on $n$ vertices, we are trying to count the number of ways to label the vertices $1$ to $n$ so that deleting them sequentially in that order never disconnects the graph. …
- 10.1k
2
votes
A special class of regular languages: "circular" languages. Is it known?
For deciding whether a language is "circular", you can just take the normalized DFA for the language (where the states correspond to sets of possible different completions). In that normalized DFA, a …
- 10.1k
20
votes
Accepted
Does this knot invariant distinguish trefoil chiralities?
I'm very curious where this came up. In any case, the answer to the first question is yes, it does distinguish these trefoils; you found the minimal representatives.
Let $a_0,\dots,a_{N-1}$ be the r …
- 10.1k
3
votes
Is the following two-dimensional graph likely to be globally rigid?
jc's answer touches most of the bases. Let me just clear up a few points.
You can, in fact, give concrete bounds on the probability a graph with vertices chosen from a finite grid will fail to be gen …
- 10.1k