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Results tagged with graph-theory
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user 105264
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
1
answer
133
views
Generalizations of a theorem of Edmonds/Tutte on existence of a perfect matching in a graphs
It is well known that for a bipartite graph $G$ with bi-adjacency matrix $A$, then $\det A \neq 0$ (as a polynomial) iff $G$ has a perfect matching (there is a similar result for general graphs with T …
- 18.7k
1
vote
1
answer
111
views
Removing a face from 4-connected planar graph
After removing a face (vertices along with edges) of a 4-connected planar graph, is the remaining graph 4-connected? Alternatively under what conditions is this true?
- 4,219
2
votes
0
answers
41
views
graphs which have polynomial bounded number of cycles
How does the graph class defined as those graphs which have polynomial (or quasi polynomial) bounded number of cycles look? (in number of vertices)
I suspect it will rather non-interesting as somethin …
- 129
3
votes
1
answer
232
views
Some questions about induced subgraphs of the directed hypercube graph
Let $Q^n$ be the hypercube graph in $n$ dimensions. Hao Huang famously showed that any induced subgraph on more than $2^{n-1}$ must have maximum degree $ \geq \sqrt{n}$. It is also known that this bou …
- 2,621
2
votes
1
answer
105
views
Exhaustive list of small graphs for which $\frac{\alpha(G)\omega(G)}{n}$ is small?
I am looking for a list of small graphs (say on less than 10 vertices) for which the parameter $p(G) = \frac{\alpha(G) \omega(G)}{n}$ is small. Here $\alpha(G)$ and $\omega(G)$ is the size of the larg …
- 3,499
0
votes
2
answers
115
views
Why is a plane graph Delaunay realizable if stellating a face makes the graph inscribable?
I have come across the following lemma in several papers (for instance see lemma 2.2 in this) (and some authors state this the proof immediately follows from basic properties of the stereographic proj …
2
votes
1
answer
150
views
Explicitly known graph families where the product of the size of biggest independent set and...
Are there explicit constructions of graph families with the following property:
$G_n$ is the graph on $n$ vertices in the family, $\omega(G_n)$ is the size of the biggest clique in the graph $G_n$, $\ …
- 79.9k