The edge density of 4-critical planar graphs

Abstract

Several constructions of 4-critical planar graphs are given. These provide answers to two questions of B. Grünbaum and give improved bounds for the maximum edge density of such graphs.

This is a preview of subscription content, access via your institution.

References

  1. [1]

    G. A. Dirac: A theorem of R. L. Brooks and a conjecture of H. Hadwiger,Proc. Lond. Math. Soc. 7 (1957), 161–195.

    Google Scholar 

  2. [2]

    T. Gallai: Critical Graphs,Theory of Graphs and its Applications (Proc. Symp. Smolenice, 1963), Publ. House Czech. Acad. Sci., Prague 1964, 43 45.

  3. [3]

    B. Grünbaum: The edge density of 4-critical planar graphs,Combinatorica,8 (1988), 137–139.

    Google Scholar 

  4. [4]

    Gy. Hajós: Über ein Konstruktion nichtn-färbbarer Graphen,Wiss. Z. Martin-Luther Univ. Halle-Wittenberg Math-Natur. Reiche 10 (1961), 116–117.

    Google Scholar 

  5. [5]

    G. Koester: Note to a problem of T. Gallai and G. A. Dirac,Combinatorica,5 (1985), 227–228.

    Google Scholar 

Download references

Author information

Affiliations

Authors

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Abbott, H.L., Zhou, B. The edge density of 4-critical planar graphs. Combinatorica 11, 185–189 (1991). https://doi.org/10.1007/BF01205071

Download citation

AMS subject classification (1980)

  • Primary 05 C 15
  • Secondary 05 C 35