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Edge-Maximal Graphs on Surfaces

Published online by Cambridge University Press:  20 November 2018

Colin McDiarmid  and
David R. Wood
Colin McDiarmid
Affiliation:
Department of Statistics, University of Oxford, United Kingdom email: cmcd@stats.ox.ac.uk
David R. Wood
Affiliation:
Department of Statistics, University of Oxford, United Kingdom email: cmcd@stats.ox.ac.uk
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Abstract

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We prove that for every surface $\Sigma $ of Euler genus $g$ , every edge-maximal embedding of a graph in $\Sigma $ is at most $O(g)$ edges short of a triangulation of $\Sigma $ . This provides the first answer to an open problem of Kainen (1974).

Keywords

05C10graphsurfaceembedding

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 70 , Issue 4 , 01 August 2018 , pp. 925 - 942
Copyright
Copyright © Canadian Mathematical Society 2018

References

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