Just Accepted This paper has been accepted to be published in the JGAA Special issue on Selected papers from the Twenty-seventh International Symposium on Graph Drawing and Network Visualization, GD 2019. The paper will receive a volume, an issue number, and page numbers when the whole special issue will be published. Recognizing Stick Graphs with and without Length Constraints Steven Chaplick, Philipp Kindermann, Andre Löffler, Florian Thiele, Alexander Wolff, Alexander Zaft, and Johannes Zink Vol. 0, no. 0, pp. 0-0, 0. Regular paper. Abstract Stick graphs are intersection graphs of horizontal and vertical line segments that all touch a line of slope $-1$ and lie above this line. De Luca et al. [De Luca et al. GD'18] considered the recognition problem of stick graphs when no order is given ($\textsf{STICK}$), when the order of either one of the two sets is given ($\textsf{STICK}_{\textsf A}$), and when the order of both sets is given ($\textsf{STICK}_{\textsf{AB}}$). They showed how to solve $\textsf{STICK}_{\textsf{AB}}$ efficiently. In this paper, we improve the running time of their algorithm, and we solve $\textsf{STICK}_{\textsf A}$ efficiently. Further, we consider variants of these problems where the lengths of the sticks are given as input. We show that these variants of $\textsf{STICK}$, $\textsf{STICK}_{\textsf A}$, and $\textsf{STICK}_{\textsf{AB}}$ are all NP-complete. On the positive side, we give an efficient solution for $\textsf{STICK}_{\textsf{AB}}$ with fixed stick lengths if there are no isolated vertices. Submitted: November 2019. Reviewed: January 2020. Revised: February 2020. Accepted: March 2020. Final: March 2020. Appeared on-line: March 2020. Communicated by Daniel Archambault and Csaba D. Tóth article (PDF) BibTeX