Adding Edges to Increase the Chromatic Number of a Graph

Alexandr Kostochka, Jaroslav Nešetřil

Research output: Contribution to journalArticle


If n ≤ k + 1 and G is a connected n-vertex graph, then one can add edges to G so that the resulting graph contains the complete graph K k+1. This yields that for any connected graph G with at least k + 1 vertices, one can add edges to G so that the resulting graph has chromatic number > k. A long time ago, Bollobás suggested that for every k ≤ 3 there exists a k-chromatic graph Gk such that after adding to it any-1 edges, the chromatic number of the resulting graph is still k. In this note we prove this conjecture.

Original languageEnglish (US)
Pages (from-to)592-594
Number of pages3
JournalCombinatorics Probability and Computing
Issue number4
StatePublished - Jul 1 2016


ASJC Scopus subject areas

  • Theoretical Computer Science
  • Statistics and Probability
  • Computational Theory and Mathematics
  • Applied Mathematics

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