All Questions
Tagged with co.combinatorics embeddings
5 questions
1
vote
1
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83
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Finite graph not embeddable in $H(n,2)$
Let $n\in\mathbb{N}$ and consider $x,y \in\{0,1\}^n$. The Hamming distance of $x,y$ is defined by $$d_H(x,y) = |\{i\in \{0,\ldots, n-1\}:x_i\neq y_i\}|.$$
For $n\geq 2$ let $H(n,2)$ be the graph given ...
4
votes
2
answers
232
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Number of non-equivalent graph embeddings
Given a graph $G$, there is a minimal integer $g$ associated with it which captures the minimum genus a surface needs to have so that $G$ embeds in the surface without edge crossings.
Is there a way ...
2
votes
1
answer
137
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VLSI circuit embeddings
In the following paper by Valiant
http://www.computer.org/csdl/trans/tc/1981/02/06312176.pdf
He shows under theorem 2 (at the bottom of the second page) that any planar graph $G$ of degree 3 or 4 ...
10
votes
1
answer
403
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Are there non-trivial graphs that uniquely embed to hypercubes?
The $n$-dimensional hypercube is the graph formed by $0$-$1$ sequences of length $n$ where two vertices are adjacent if they differ at only one place.
The weight of a sequence is the number of $1$'s ...
14
votes
0
answers
416
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Monotone embedding of complete binary tree in hypercube
Embedding different graphs, especially binary trees, in the hypercube has a huge literature. However, I could not find anything if we restrict the embedding to be monotone. So I would like to ...