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.
Similar content being viewed by others
References
G. A. Dirac: A theorem of R. L. Brooks and a conjecture of H. Hadwiger,Proc. Lond. Math. Soc. 7 (1957), 161–195.
T. Gallai: Critical Graphs,Theory of Graphs and its Applications (Proc. Symp. Smolenice, 1963), Publ. House Czech. Acad. Sci., Prague 1964, 43 45.
B. Grünbaum: The edge density of 4-critical planar graphs,Combinatorica,8 (1988), 137–139.
Gy. Hajós: Über ein Konstruktion nichtn-färbbarer Graphen,Wiss. Z. Martin-Luther Univ. Halle-Wittenberg Math-Natur. Reiche 10 (1961), 116–117.
G. Koester: Note to a problem of T. Gallai and G. A. Dirac,Combinatorica,5 (1985), 227–228.
Author information
Authors and Affiliations
Rights 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
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01205071