Abstract
It is shown that a planar graph withouti-circuits, 4 ≤i ≤ 9, is 3-colorable. This result strengthens the result obtained by H.L. Abbott and B. Zhou.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abbott, H.L., Zhou, B.: On small faces in 4-critical planar graphs. Ars Combin.32, 203–207 (1991)
Aksionov, V.A., Melnikov, L.S.: Essay on the theme: The three color problem. Combinatorics, Colloq. Math. Soc. János Bolyai18, 23–34 (1976)
Aksionov, V.A., Melnikov, L.S.: Some counterexamples associated with the three color problem. J. Comb. Theory ser.B28, 1–9 (1980)
Erdös, P.: informal discussion during the conference “Quo Vadis, Graph Theory?” University of Alaska, Fairbanks, Alaska, August (1990)
Steinberg, R.: The state of the three color problem. Ann. Discrete Math.55, 211–248 (1993)
Author information
Authors and Affiliations
Additional information
The author's research was partially supported by the Office of Naval Research, Grant number N00014-92-J-1965.
Rights and permissions
About this article
Cite this article
Sanders, D.P., Zhao, Y. A note on the three color problem. Graphs and Combinatorics 11, 91–94 (1995). https://doi.org/10.1007/BF01787424
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01787424