Adding random edges to dense graphs

This paper investigates the addition of random edges to arbitrary dense graphs; in particular, we determine the number of random edges required to ensure various monotone properties including the appearance of a fixed size clique, small diameter and $k$-connectivity.

[1]  P. Erdos,et al.  On the evolution of random graphs , 1984 .

[2]  M. Simonovits,et al.  Szemeredi''s Regularity Lemma and its applications in graph theory , 1995 .

[3]  Alan M. Frieze,et al.  On the independence number of random graphs , 1990, Discret. Math..

[4]  Svante Janson,et al.  Random graphs , 2000, Wiley-Interscience series in discrete mathematics and optimization.

[5]  Béla Bollobás,et al.  The Diameter of a Cycle Plus a Random Matching , 1988, SIAM J. Discret. Math..

[6]  Tom Bohman,et al.  How many random edges make a dense graph hamiltonian? , 2003, Random Struct. Algorithms.

[7]  Reinhard Diestel,et al.  Graph Theory , 1997 .

[8]  B. Bollobás.  The evolution of random graphs , 1984 .

[9]  Alan M. Frieze,et al.  Random graphs , 2006, SODA '06.

[10]  Béla Bollobás,et al.  The chromatic number of random graphs , 1988, Comb..

[11]  E. Szemerédi.  Regular Partitions of Graphs , 1975 .