On decidability of hyperbolicity
Zden\v{e}k Dvo\v{r}\'ak, Luke Postle
TL;DR
This paper investigates the decidability of hyperbolicity in graphs, demonstrating that many coloring problems on surface-embedded graphs can be solved by examining a finite set of configurations.
Contribution
It introduces a method to determine hyperbolicity by analyzing a finite number of configurations, advancing understanding of graph coloring problems on surfaces.
Findings
Coloring problems on surface graphs are decidable via finite configuration inspection.
A broad class of coloring problems can be resolved algorithmically.
Finite configuration analysis simplifies complex surface graph coloring issues.
Abstract
We prove that a wide range of coloring problems in graphs on surfaces can be resolved by inspecting a finite number of configurations.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Differential Equations and Dynamical Systems · advanced mathematical theories