Abstract
We consider the minimum number of edges in ak-edge-connected graph of ordern with chromatic number at leastc, obtaining the optimal bounds in most cases.
Similar content being viewed by others
References
Bondy, J.A., Murty, U.S.R.: Graph Theory with Applications. North-Holland, 1976
Dirac, G.A.: The structure ofk-chromatic graphs, Fund. Math.40, 42–55 (1953)
Dirac, G.A.: A theorem of R.L. Brooks and a conjecture of H. Hadwiger, Proc. Lond. Math. Soc.17, 161–195(1957)
Dirac, G.A.: The number of edges in critical graphs, J. Reine Angew Math.268/269, 150–164(1974)
Harary, F.: The maximum connectivity of a graph, Proc. Nat. Acad. Sci. U.S.A.48, 1142–1146(1962)
Toft, Graph colouring theory, Handbook of Combinatorics, (to be published)
Tomescu, I.: R. Acad. Sci. Paris A272 (1971), 1301–1303
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bhasker, J., Samad, T. & West, D.B. Size, chromatic number, and connectivity. Graphs and Combinatorics 10, 209–213 (1994). https://doi.org/10.1007/BF02986667
Issue Date:
DOI: https://doi.org/10.1007/BF02986667