Radius, diameter, and minimum degree

Abstract We give asymptotically sharp upper bounds for the maximum diameter and radius of (i) a connected graph, (ii) a connected trangle-free graph, (iii) a connected C 4 -free graph with n vertices and with minimum degree δ, where n tends to infinity. Some conjectures for K r -free graphs are also stated.

[1]  W. G. Brown.  On Graphs that do not Contain a Thomsen Graph , 1966, Canadian Mathematical Bulletin.

[2]  A. Rényii,et al.  ON A PROBLEM OF GRAPH THEORY , 1966 .

[3]  Béla Bollobás,et al.  The Diameter of Graphs: a survey , 1981 .

[4]  B. Bollobás,et al.  Extremal Graph Theory , 2013 .