Hypercubes and Multicommodity Flows

  • Authors:
  • B. Yu;J. Cheriyan;P. E. Haxell

  • Affiliations:
  • -;-;-

  • Venue:
  • SIAM Journal on Discrete Mathematics
  • Year:
  • 1997

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Abstract

The average degree of a subgraph $H$ of the $r$-dimensional hypercube $Q_r$ equals at most the maximum Hamming distance of any two nodes in $H$. A corollary is that the minimum number of edges to delete from $Q_r$ such that any two nodes at Hamming distance $\ell$ are separated is $(r+1-\ell) 2^{r-1}$. This corollary has applications to multicommodity flows.