The dichromatic number of a digraph D is the minimum number of colors of a vertex coloring of D such that D has no monochromatic cycles, the dichromatic number is an extension of the chromatic number to the class of digraphs. The Hajós join is a tool to obtain r-chromatic graphs, using the dichromatic number, J. Bang-Jensen et. al. extended the Hajós join to digraphs, and thus obtained a tool to obtain r-dichromatic digraphs. J. Bang-Jensen et. al. posed in 2020 the problem of how to obtain the symmetric cycle of length 5 from symmetric cycles of length 3. We recently solved this problem by applying a genetic algorithm. In this article, we generalize the construction of the symmetric cycle of length 5 and determine the computational complexity as Θ(n ln(n)).

Abstract The User Interface Transition Diagram (UITD) is a simplified modeling notation to describe the transitions between the UIs of a software system. It is designed to be used for customer‐developer s improving the models. This study investigates (i) which concepts of the UITD language are easy to understand and which ones require more effort to be understood and (ii) to what extent UITD comprehensibility depends on the user's programming skill level. A questionnaire was applied to a group of 334 non‐developers after they received a very brief explanation of the UITD concepts. The results were analyzed using statistical methods. The overall average score of the group was 70.42%, which is quite acceptable considering the briefness of the explanation. We observed a very low correlation between the subjects' programming skill level and their scores. This suggests that, even for people who have little or no programming skills, the entirety of the UITD symbols and concepts should quickly be understood with little further training.