orthogonality graph

The Independence Number of the Orthogonality Graph — Or: The Usefulness of Literature Study

Let {X} be the orthogonality graph, that is the graph with {\{ -1, 1 \}^n} as vertices with two vertices adjacent if they are orthogonal. So {x, y \in \{ -1, 1 \}^n} are adjacent if {x \cdot y = x_1y_1 + x_2y_2 + \ldots + x_ny_n = 0}. There are many publications which investigate this problem. The aim of this post is two fold:

  1. To summarize the state of the art.
  2. To demonstrate how careful literature study is helpful to obtain results.