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The chromatic connectivity of graphs

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Abstract

A graphG ischromatically k-connected if every vertex cutset induces a subgraph with chromatic number at leastk. This concept arose in some work, involving the third author, on Ramsey Theory. (For the reference, see the text.) Here we begin the study of chromatic connectivity for its own sake. We show thatG is chromaticallyk-connected iff every homomorphic image of it isk-connected. IfG has no triangles then it is at most chromatically 1-connected, but we prove that the Kneser graphs provide examples ofK 4-free graphs with arbitrarily large chromatic connectivity. We also verify thatK 4-free planar graphs are at most chromatically 2-connected.

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References

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Simon Fraser University, V5A 1S6, Burnaby, B.C., Canada

    C. D. Godsil

  2. Department of Mathematics, Dalhousie University, Halifax, Nova Scotia, Canada

    R. Nowakowski

  3. KAM MFF KU, Charles University, Malostranské nám. 25, 118 00, Praha 1, Czechoslovakia

    J. Nešetřil

Authors
  1. C. D. Godsil
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  2. R. Nowakowski
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  3. J. Nešetřil
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Additional information

This work was supported by grants from NSERC of Canada.

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Godsil, C.D., Nowakowski, R. & Nešetřil, J. The chromatic connectivity of graphs. Graphs and Combinatorics 4, 229–233 (1988). https://doi.org/10.1007/BF01864163

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  • DOI: https://doi.org/10.1007/BF01864163

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