On embeddings of half-cube graphs in half-spin Grassmannians

Details On embeddings of half-cube graphs in half-spin Grassmannians On embeddings of half-cube graphs in half-spin Grassmannians

2011-06-27

arxiv.org/abs/1106.5435v1

Mathematics

Combinatorics

Scientific paper

We investigate isometric embeddings of the $m$-dimensional half-cube graph $1/2 H_m$ in the half-spin Grassmannians associated with a polar space of type $\textsf{D}_n$ with $n\ge m\ge 4$. We establish the following: if a such embedding can be extended to an embedding of the hypercube graph $H_m$ in the dual polar space (the latter embedding is not assumed to be isometric) and $m$ is even then the image is an apartment in a parabolic subspace.

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