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Results tagged with graph-theory
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user 23980
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.
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Isometric path cover number of the 2 dimensional grid graph
I am looking for a proof of the fact that at least $2n/3$ isometric paths (i.e. shortest paths between the end points) are required to cover the vertices of the $n\times n$ grid graph (i.e. Cartesian …
- 23.7k
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Regarding rigid graphs in the plane
Quoting from the book (page 272) Graphs and Geometry by Lovasz, we have the following theorems regarding the characterization of rigid graphs in the pane.
Theorem 1: A graph $G$ is rigid in the plane …
- 1,305
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Checking existence of a non-crossing Hamiltonian path in geometric graphs
I am interested in the following computational problem. Given a geometric graph (i.e, a graph drawn in the plane so that its vertices are represented by points in general position and its edges are st …
- 4,219
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Independence number of a grid like graph
Given natural numbers $n$ and $k$, let $G_{n,k}$ denote the simple graph whose vertex set is $\{1,2,\ldots ,n\}$ and there is an edge between $i$ and $j$ when $|i-j|\leq k$. I am interested in the ind …
- 1,305
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Number of spanning trees from the automorphism group
What information does the automorphism group $\mathrm{Aut}(G)$ of a graph $G$ give us about the number of it's spanning trees?
If not in general, can anything be said about some special cases, for e …
- 1,305
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Self complementary cartesian products
Given two graphs $G$ and $H$ is there a nice way to check whether the cartesian product $G\Box H$ is self complementary without directly computing its complement and searching for isomorphism? For ex …
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