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Results tagged with graph-theory
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user 8075
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.
15
votes
2
answers
1k
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When does graph minor containment imply subgraph containment?
Consider a path of length 3. Any graph G which contains this graph as a minor must also contain it as a subgraph. For paths of any length this is easy to prove.
In general this happens for any graph …
- 1,332
4
votes
Accepted
Finding a subgraph with slightly large size in planar graphs
I remember thinking about this a while ago, and stopped because it seemed unlikely that $log^2 n$ paths can be found in polynomial time. This was my argument, if I remember correctly.
The best know …
- 1,332
5
votes
1
answer
389
views
Ref request: A graph G contains H as a minor iff it contains one of finitely many graphs as ...
For definitions of graph minors and topological minors, see wikipedia's article on graph minors.
Theorem: For every graph H, there is a finite set of graphs, say S(H), such that G contains H as a min …
- 1,332
9
votes
What are some good examples of non-monotone graph properties?
Some natural non-monotone properties:
The property of being regular
The property of being a tree
The property of being Eulerian
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