A RAC graph is one admitting a RAC drawing, that is, a polyline drawing in which each crossing occurs at a right angle. Originally motivated by psychological studies on readability of graph layouts, RAC graphs form one of the most prominent graph classes in beyond planarity. In this work, we study a subclass of RAC graphs, called axis-parallel RAC (or apRAC, for short), that restricts the crossings to pairs of axis-parallel edge-segments. apRAC drawings combine the readability of planar drawings with the clarity of (non-planar) orthogonal drawings. We consider these graphs both with and without bends. Our contribution is as follows: (i) We study inclusion relationships between apRAC and traditional RAC graphs. (ii) We establish bounds on the edge density of apRAC graphs. (iii) We show that every graph with maximum degree 8 is 2-bend apRAC and give a linear time drawing algorithm. Some of our results on apRAC graphs also improve the state of the art for general RAC graphs. We conclude our work with a list of open questions and a discussion of a natural generalization of the apRAC model.

翻译：RAC图是指存在RAC绘图的图，即每条交叉点均为直角的折线绘图。该图类最初源于对图形布局可读性的心理学研究，现已成为平面性之外最突出的图类之一。本文研究RAC图的一个子类——轴向平行RAC图（简称apRAC），该子类将交叉限制为仅发生在轴向平行的边段之间。apRAC绘图兼具平面绘图的可读性与（非平面）正交绘图的清晰性。我们分别研究带折点和无折点两种情况下的此类图。主要贡献包括：(i) 探究apRAC图与传统RAC图的包含关系；(ii) 建立apRAC图边密度的上下界；(iii) 证明所有最大度不超过8的图均为2折点apRAC图，并给出线性时间绘图算法。部分apRAC图的研究成果也改进了一般RAC图的现有结论。最后，我们提出若干开放性问题，并讨论apRAC模型的自然推广。