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2
votes
0
answers
59
views
Maximum number of edges on $2^{k-1}+s$ vertices of a $k$-dimensional cube?
Let $k$ be an even number. For a $k$-dimensional cube (http://mathworld.wolfram.com/HypercubeGraph.html) $Q_k$, let $G$ be a subgraph of $Q_k$ with $2^{k-1}+s$ vertices, for $1\le s\le 2^{k-1}-1$. I a …
1
vote
1
answer
66
views
Existence of dense graph with relatively small codegree?
Let $n$ be some parameter tending to infinity. I am wondering does there exists some kind of graphs $G$ on vertex-set $[n]$ with maximum degree less than $D$, so that
$D\ge n/w_1(n)$,
$e_G$, the nu …