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Density of 5/2-critical graphs

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Abstract

A graph G is 5/2-critical if G has no circular 5/2-coloring (or equivalently, homomorphism to C 5), but every proper subgraph of G has one. We prove that every 5/2-critical graph on n ≥ 4 vertices has at least

$$\frac{{5n - 2}}{4}$$

edges, and list all 5/2-critical graphs achieving this bound. This implies that every planar or projective-planar graph of girth at least 10 is 5/2-colorable.

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Author information

Authors and Affiliations

  1. Charles University, Prague, Czech Republic

    Zdeněk Dvořák

  2. University of Waterloo, Waterloo, Canada

    Luke Postle

Authors
  1. Zdeněk Dvořák
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  2. Luke Postle
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Corresponding author

Correspondence to Zdeněk Dvořák.

Additional information

Supported by project GA14-19503S (Graph coloring and structure) of Czech Science Foundation.

Partially supported by NSERC under Discovery Grant No. 2014-06162, the Ontario Early Researcher Awards program and the Canada Research Chairs program.

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Dvořák, Z., Postle, L. Density of 5/2-critical graphs. Combinatorica 37, 863–886 (2017). https://doi.org/10.1007/s00493-016-3356-3

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  • DOI: https://doi.org/10.1007/s00493-016-3356-3

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