2023/10/30 by Sandi Klavžar, Jing Tian, Klavžar, Sandi +3
Computer Science · Economics, Econometrics and Finance · #05C12 #05C57 #05C69 #Artificial Intelligence in Games #Combinatorics (math.CO) #FOS: Mathematics #Sports Analytics and Performance
paper · pdf · doi:10.48550/arxiv.2310.19949
openalex publication_date 2023/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper considers a game version of the general position problem in which a general position set is built through adversarial play. Two players in a graph, Builder and Blocker, take it in turns to add a vertex to a set, such that the vertices of this set are always in general position. The goal of Builder is to create a large general position set, whilst the aim of Blocker is to frustrate Builder's plans by making the set as small as possible. The game finishes when no further vertices can be added without creating three-in-a-line and the number of vertices in this set is the game general position number. We determine this number for some common graph classes and provide sharp bounds, in particular for the case of trees. We also discuss the effect of changing the order of the players.