All Questions
Tagged with graph-minors reference-request
9 questions
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Does the purported proof of Rota's conjecture provide an algorithm for calculating the forbidden minors of matroids over arbitrary finite fields?
About six years ago there was a proof announced and later outlined in a notice from AMS. However right now I can only seem to find forbidden minor characterizations for matroids linearly ...
- 2,506
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Directed graph minor theorems
In proving the graph minor theorem, Robertson and Seymour proved a stronger statement, namely that the directed graph minor theorem is true, using the definition
A directed graph is a minor of ...
- 612
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Disjoint paths between four vertices
Consider the following property of an undirected graph: For any four distinct vertices $a,b,c,d$, there is a path from $a$ to $b$ and a path from $c$ to $d$ such that the two paths do not share any ...
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What is a hypergraph minor?
Is there a theory of hypergraph minors? I could only find some attempts to define them at papers/theses, whose main topic was something else. What would be a useful definition? Does the hypergraph ...
- 18.7k
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Flat or linkless embeddings of graph with fixed projection
The problem of finding whether a given planar diagram of a graph, with over- and under-crossings, is a linkless embedding or not has unknown complexity (Kawarabayashi et al., 2010). My first question ...
- 221
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Does anyone know a specific polynomial-time algorithm to detect if a given signed graph contains an odd-K4 as a signed minor?
By signed graph, I mean each edge is designated either odd or even (e.g. as in Guenin's result for weakly bipartite graphs).
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Is there a polynomial-time algorithm to check if a signed graph contains an odd-K5 minor?
I suspect this exists, if anyone has a reference please that would be very helpful.
By signed graph, I mean each edge is designated either odd or even (e.g. as in Guenin's result for weakly bipartite ...
- 311
4
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Contracting a planar graph to a (multiply-edged)-tree
Given a planar graph (no loops, no multiple edge), is it always possible to perform edge contractions* in order to obtain a graph $T$ which has no loops, and if one ignores parallel edges, $T$ is a ...
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Ref request: A graph G contains H as a minor iff it contains one of finitely many graphs as a topological minor
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 ...
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