Note: Linear spaces with small generated subspaces

Authors:
Peter Dukes;Alan C. H. Ling
Affiliations:
Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada;Department of Computer Science, University of Vermont, Burlington, Vermont 05405, USA
Venue:
Journal of Combinatorial Theory Series A
Year:
2009

Citing 4
Cited 0

Note: On a Problem of R. Häggkvist Concerning Edge-Colouring of Bipartite Graphs

Combinatorica
Handbook of Combinatorial Designs, Second Edition (Discrete Mathematics and Its Applications)

Handbook of Combinatorial Designs, Second Edition (Discrete Mathematics and Its Applications)
Note edge-colourings of K n,n with no long two-coloured cycles

Combinatorica
On the structure of uniform one-factorizations from starters in finite fields

Finite Fields and Their Applications

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Abstract

The dimension of a linear space is the maximum positive integer d such that any d of its points generate a proper subspace. Given n, d, s, we consider linear spaces on n points such that any d points generate subspaces of size at most s. Certain design-theoretic constructions and applications are investigated. In particular, one consequence is the existence of proper n-edge-colourings of both K"n"+"1 (for n odd) and K"n","n with a constant bound on the length of two-colored cycles.