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Solution to a Problem of Grünbaum on the Edge Density of 4-Critical Planar Graphs

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Abstract

We show that \(\limsup |E(G)|/|V(G)| = 2.5\) over all 4-critical planar graphs G, answering a question of Grünbaum from 1988.

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Acknowledgements

The authors thank both referees for valuable comments that helped improved the presentation and clarity of arguments. Zdeněk Dvořák was supported by project 22-17398S (Flows and cycles in graphs on surfaces) of Czech Science Foundation. Carl Feghali was supported by the French National Research Agency under research Grant ANR DIGRAPHS ANR-19-CE48-0013-01.

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Authors and Affiliations

  1. Computer Science Institute (CSI) of Charles University, Prague, Czech Republic

    Zdeněk Dvořák

  2. Univ Lyon, EnsL, CNRS, LIP, 69342, Lyon Cedex 07, France

    Carl Feghali

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  1. Zdeněk Dvořák
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  2. Carl Feghali
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Correspondence to Carl Feghali.

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Dvořák, Z., Feghali, C. Solution to a Problem of Grünbaum on the Edge Density of 4-Critical Planar Graphs. Combinatorica (2024). https://doi.org/10.1007/s00493-024-00100-8

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  • DOI: https://doi.org/10.1007/s00493-024-00100-8

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