All Questions
6 questions with no upvoted or accepted answers
24
votes
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760
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How much of the plane is 4-colorable?
In 1981, Falconer proved that the measurable chromatic number of the plane is at least 5. That is, there are no measurable sets $A_1,A_2,A_3,A_4\subseteq\mathbb{R}^2$, each avoiding unit distances, ...
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4
votes
0
answers
230
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Is this case of Barnette's Conjecture known?
Context: Barnette's Conjecture is that every bipartite cubic polyhedral graph is Hamiltonian. I have been interested by this problem for a long time, and I recently came up with a result. From my ...
- 3,499
3
votes
0
answers
144
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Counting homologically non-trivial and trivial cycles in $n \times n$ square lattice torus of a given length $l \geq n$
This should be a fairly standard question but I can't really seem to find a reference.
Consider an $n \times n$ square lattice torus $\mathbb T$. Given a length $l \geq n$, what is the number of ...
- 269
3
votes
0
answers
142
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Dimension of convex arrangements for hypergraphs
Suppose you have a hypergraph H on n vertices. Let d be the smallest integer such that we can find an arrangement A of convex subsets in Rd so that H represent the intersections of sets in A.
Has ...
- 4,586
2
votes
0
answers
65
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Structure Theory for Tree Decompositions
I that $G=(V,E,W)$ is a weighted graph with positive edge weights and a finite set of vertices $K$. Let $0\le k,M\le K$ be a fixed integer.
Is is known when $G$ admits the following type of ...
- 21
1
vote
0
answers
77
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Non-adjacent Pair of Edges with Minimal Weight Sum
Given an weighted, undirected Graph $G(V,E)$ without loops or parallel edges,
what is the complexity of determining a pair of non-adjacent edges, whose sum of weights is w.l.o.g. minimal?
is that ...
- 13.2k