On the edge-density of 4-critical graphs


Gallai conjectured that every 4-critical graph on n vertices has at least 5/3n-2/3 edges. We prove this conjecture for 4-critical graphs in which the subgraph induced by vertices of degree 3 is connected.

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Corresponding author

Correspondence to Babak Farzad.

Additional information

Much of this research was done when the author was a graduate student at the University of Toronto and a postdoctoral fellow at McGill University. This research is supported by NSERC and University of Toronto Fellowship.

This research is supported in part by NSERC and a Sloan Research Fellowship.

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Farzad, B., Molloy, M. On the edge-density of 4-critical graphs. Combinatorica 29, 665–689 (2009). https://doi.org/10.1007/s00493-009-2267-y

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Mathematics Subject Classification (2000)

  • 05C15