Geometry and Generation of a New Graph Planarity Game

TL;DR

This paper introduces Swap Planarity, a new graph game focused on achieving a planar graph through vertex swaps, and analyzes its complexity, generation, and quality criteria using graph theory and computational geometry.

Contribution

It presents the design, analysis, and instance generation method for the novel Swap Planarity game, combining graph theory, geometry, and complexity analysis.

Findings

Effective method for generating high-quality puzzle instances

Analysis of the game's complexity and properties

Experimental validation of the generation process

Abstract

We introduce a new abstract graph game, Swap Planarity, where the goal is to reach a state without edge intersections and a move consists of swapping the locations of two vertices connected by an edge. We analyze this puzzle game using concepts from graph theory and graph drawing, computational geometry, and complexity. Furthermore, we specify quality criteria for puzzle instances, and describe a method to generate high-quality instances. We also report on experiments that show how well this generation process works.