Graphs and Combinatorics

, Volume 32, Issue 6, pp 2525–2539 | Cite as

Computing Planarity in Computable Planar Graphs

Original Paper

Abstract

A graph is computable if there is an algorithm which decides whether given vertices are adjacent. Having a procedure for deciding the edge set might not help compute other properties or features of the graph, however. The goal of this paper is to investigate the extent to which features related to the planarity of a graph might or might not be computable. We propose three definitions for what it might mean for a computable graph to be computably planar and for each build a computable planar graph which fails to be computably planar. We also consider these definitions in the context of highly computable graphs, those for which there is an algorithm which computes the degree of a given vertex.

Keywords

Infinite graphs Planar graphs Computability theory Planar embeddings 

Mathematics Subject Classification

05C10 05C63 03D45 

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Copyright information

© Springer Japan 2016

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity of Northern ColoradoGreeleyUSA

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