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Results tagged with graph-theory
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user 18086
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.
20
votes
Accepted
A Ramsey avoidance game
This game can be described as an impartial edge colouring game on $K_n$ where creating a monochrome $K_k$ is not allowed, and the last player to make a move wins (normal play). Hence, it is equivalent …
- 1,887
1
vote
Are all almost regular graphs obvious?
Partition your graph into vertices of even degree, $N$, and vertices of odd degree, $D$. If the size of both sets is even, then you can add a matching to the set with lower degree to get a regular gra …
- 1,887
5
votes
Accepted
classify strongly regular graph with parameter (25,12,5,6)
What you're really looking for are conference graphs of order 25, which come from symmetric conference matrices of order 26. Your 15 known graphs are the Paulus graphs on 26 nodes, and the 10 are Paul …
- 1,887
5
votes
Traversing the infinite square grid
For a one dimensional lattice, the solution with $a_n = n$ is trivial: starting from $0$, we proceed to $1, -1, 2, -2, \ldots$. After $2n$ steps, we have covered $[-n, n]$ without stepping anywhere ou …
- 1,887
8
votes
A hypercube-related graph
Conway & Sloane's "Sphere Packings, Lattices and Groups" references Coxeter's "Regular Polytopes" for the phrase "halfcube", but Coxeter only uses the notation $h\Pi_n$, saying $h$ can be taken to sta …
- 1,887