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Combinatorica

, Volume 37, Issue 5, pp 863–886 | Cite as

Density of 5/2-critical graphs

  • Zdeněk DvořákEmail author
  • Luke Postle
Original Paper

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.

Mathematics Subject Classification (2000)

05C15 

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Copyright information

© János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Charles UniversityPragueCzech Republic
  2. 2.University of WaterlooWaterlooCanada

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