List Colouring When The Chromatic Number Is Close To the Order Of The Graph

Ohba has conjectured [7] that if G has 2 χ (G)+1 or fewer vertices then the list chromatic number and chromatic number of G are equal. In this short note we prove the weaker version of the conjecture obtained by replacing 2 χ (G)+1 by \( \frac{5} {3}\chi {\left( G \right)} - \frac{4} {3}. \)

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Correspondence to Bruce Reed*.

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* This research was partially supported by DIMACS and by CNRS/NSF collaboration grant.

† Research supported in part by NSF grants DMS-0106589, CCR-9987845 and by the State of New Jersey.

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Reed*, B., Sudakov†, B. List Colouring When The Chromatic Number Is Close To the Order Of The Graph. Combinatorica 25, 117–123 (2004). https://doi.org/10.1007/s00493-005-0010-x

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Mathematics Subject Classification (2000):

  • 05C15
  • 05D40