25 research outputs found
Beyond Tryptophan Synthase: Identification of Genes That Contribute to Chlamydia trachomatis Survival during Gamma Interferon-Induced Persistence and Reactivation
On a visibility representation for graphs in three dimensions
This paper proposes a 3-dimensional visibility representation of graphs G = (V,E) in which vertices are mapped to rectangles floating in R 3 parallel to the x, y-plane, with edges represented by vertical lines of sight. We apply an extension of the Erdős-Szekeres Theorem in a geometric setting to obtain an upper bound of n = 56 for the largest representable complete graph Kn. On the other hand, we show by construction that n ≥ 22. These are the best existing bounds. We also note that planar graphs and complete bipartite graphs Km,n are representable, but that the family of representable graphs is not closed under graph minors
On a visibility representation for graphs in 3D
This paper proposes a 3-dimensional visibility representation of graphs G = (V,E) in which vertices are mapped to rectangles floating in R 3 parallel to the x,y-plane, with edges represented by vertical lines of sight. We apply an extension of the Erdös-Szekeres Theorem in a geometric setting to obtain an upper bound of n = 56 for the largest representable complete graph Kn. On the other hand, we show by construction that n>=22. These are the best existing bounds. We also note that planar graphs and complete bipartite graphs Km,n are representable, but that the family of representable graphs is not closed under graph minors