Matching Subspaces with Complementsin Finite Vector Spacesw

@inproceedings{ClarkJune1992MatchingSW,
  title={Matching Subspaces with Complementsin Finite Vector Spacesw},
  author={. Edwin ClarkJune},
  year={1992}
}
  • . Edwin ClarkJune
  • Published 1992
Let C (n; q) denote the graph whose vertices are the subspaces of the n dimensional vector space V over GF (q) and whose edges are the pairs fX; Y g where X Y = V. We show that C (n; q) has a perfect matching if and only if q is odd or n is odd. If q and n are even and q > 2 we show there exist matchings which omit only one vertex. 

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