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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.
0
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Partition of $\mathbb{F}_2^n$?
The answer to this question turns out to be negative i.e. in general it is not possible to partition the space $\mathbb{F}_2^n$ such that each partition has that property.
Consider the graph on $\mat …
2
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Partition of $\mathbb{F}_2^n$?
Consider an undirected graph $G$ with $n$ nodes denoted by $i$, $i \in [n] = \{1,2,...,n\}$. Denote the set of neighbours of node $i$ in the graph by $N(i)$.
Given that there exists a set $\mathcal{I …