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Results tagged with graph-theory
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user 22989
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
Accepted
Representation-finite implies planar for quiver algebras?
Consider path algebras $KQ$ modulo "radical square zero" relations (i.e., paths of length two are zero). It is well known that these have finite representation type if and only if the separated quiver …
- 35.2k
24
votes
Accepted
Non-isomorphic graphs with bijective graph homomorphisms in both directions between them
As vertex set, take $V=V'\cup V''$, the disjoint union of two infinite sets.
For $G$, take all edges except those joining pairs of vertices from $V''$.
For $H$, add one extra edge, between a pair of …
- 35.2k
23
votes
Accepted
Is deciding if one planar graph is dual to another really NP-hard (Wikipedia claim)?
The dual graph and medial graph depend on the choice of an embedding in the plane. The Wikipedia claim seems to be that testing whether there are choices of embeddings for which two graphs are dual is …
- 35.2k
5
votes
Accepted
Regular epimorphisms in the category of simple undirected graphs
I think the paper "A canonical factorization for graph homomorphisms", Barry Fawcett, Can J. Math. 29 (4), 1977, 738-743, answers the question.
Theorem 3 states that in $\textbf{Grph}$, strict epimor …
- 35.2k