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Results tagged with co.combinatorics
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user 105264
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
2
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1
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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 …
- 129
2
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0
answers
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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
1
vote
1
answer
111
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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?
- 129
3
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1
answer
232
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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 …
- 129
3
votes
1
answer
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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 …
- 129