Counting Strict Gridlock on Graphs
Matthew I. Jones, Zachary Winkeler

TL;DR
This paper introduces a new framework for analyzing distributed graph coloring problems related to consensus formation, focusing on counting strict gridlock colorings that prevent groups from reaching agreement.
Contribution
It defines a novel type of graph coloring called strict gridlock colorings and provides a recurrence relation to count these colorings, linking graph structure to consensus difficulty.
Findings
Developed a recurrence relation for counting gridlock colorings
Established a mathematical measure of how graph structure hinders consensus
Linked gridlock colorings to social group dynamics and network analysis
Abstract
Graph colorings have been of interest to mathematicians for a long time, but relatively recently, social scientists have also found them to be interesting tools for studying group behavior. In the last 20 years, scientists have begun to study how coloring problems can be solved by groups of individuals on a graph, which has led to new insights into network structure, group dynamics, and individual human behavior. Despite this newfound utility, the exact nature of these distributed coloring problems is not well-understood, and established mathematical tools like the chromatic polynomial miss the unique challenges that arise in these social problem-solving situations with limited information. In this paper, we provide a new framework for understanding these distributed problems by defining a new kind of graph coloring with particular relevance to consensus formation on networks, in which…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsComplex Network Analysis Techniques · Constraint Satisfaction and Optimization · Advanced Graph Theory Research
