[1]Aldous, D. (1989) An introduction to covering problems for random walks on graphs. J. Theoret. Probab. 2 87–89.

[2]Aldous, D. J. (1991) Random walk covering of some special trees. J. Math. Anal. Appl. 157 271–283.

[4]Aleliunas, R., Karp, R. M., Lipton, R. J., Lovász, L. and Rackoff, C. (1979) Random walks, universal traversal sequences, and the complexity of maze problems. In 20th Annual Symposium on Foundations of Computer Science (San Juan, Puerto Rico, 1979), IEEE, pp. 218–223.

[5]Barlow, M. T. (1985) Continuity of local times for Lévy processes. Z. Wahrsch. Verw. Gebiete 69 23–35.

[6]Bollobás, B. (1984) The evolution of random graphs. Trans. Amer. Math. Soc. 286 257–274.

[7]Borgs, C., Chayes, J. T., van der Hofstad, R., Slade, G. and Spencer, J. (2005) Random subgraphs of finite graphs I: The scaling window under the triangle condition. Random Struct. Alg. 27 137–184.

[8]Bridgland, M. F. (1987) Universal traversal sequences for paths and cycles. J. Algorithms 8 395–404.

[9]Broder, A. (1990) Universal sequences and graph cover times: A short survey. In Sequences (Naples/Positano 1988), Springer, pp. 109–122.

[10]Chandra, A. K., Raghavan, P., Ruzzo, W. L., Smolensky, R. and Tiwari, P. (1996/97) The electrical resistance of a graph captures its commute and cover times. Comput. Complexity 6 312–340.

[11]Cooper, C. and Frieze, A. (2008) The cover time of the giant component of a random graph. Random Struct. Alg. 32 401–439.

[12]Ding, J., Kim, J. H., Lubetzky, E. and Peres, Y. Anatomy of a young giant component in the random graph. *Random Struct. Alg*., to appear. Available at: http://arxiv.org/abs/0906.1839. [13]Ding, J., Kim, J. H., Lubetzky, E. and Peres, Y. (2010) Diameters in supercritical random graphs via first passage percolation. Combin. Probab. Comput. 19 729–751.

[15]Dudley, R. M. (1967) The sizes of compact subsets of Hilbert space and continuity of Gaussian processes. J. Funct. Anal. 1 290–330.

[16]Erdős, P. and Rényi, A. (1959) On random graphs I. Publ. Math. Debrecen 6 290–297.

[17]Erdős, P. and Rényi, A. (1961) On the evolution of random graphs. Bull. Inst. Internat. Statist. 38 343–347.

[18]Feige, U. (1995) A tight upper bound on the cover time for random walks on graphs. Random Struct. Alg. 6 51–54.

[19]Feige, U. (1995) A tight lower bound on the cover time for random walks on graphs. Random Struct. Alg. 6 433–438.

[20]Feller, W. (1971) An Introduction to Probability Theory and its Applications, Vol. II, 2nd edition, Wiley.

[21]Heydenreich, M. and van der Hofstad, R. (2007) Random graph asymptotics on high-dimensional tori. Comm. Math. Phys. 270 335–358.

[22]Heydenreich, M. and van der Hofstad, R. Random graph asymptotics on high-dimensional tori II: Volume, diameter and mixing time. *Probability Theory and Related Fields*, to appear.

[23]Janson, S., Łuczak, T. and Rucinski, A. (2000) Random Graphs, Wiley-Interscience Series in Discrete Mathematics and Optimization, Wiley-Interscience.

[24]Jonasson, J. (2000) Lollipop graphs are extremal for commute times. Random Struct. Alg. 16 131–142.

[25]Kahn, J., Kim, J. H., Lovász, L. and Vu, V. H. (2000) The cover time, the blanket time, and the Matthews bound. In 41st Annual Symposium on Foundations of Computer Science (Redondo Beach 2000), IEEE Comput. Soc. Press, pp. 467–475.

[26]Karlin, Anna R. and Raghavan, P. (1995) Random walks and undirected graph connectivity: A survey. In Discrete Probability and Algorithms (Minneapolis 1993), Vol. 72 of *IMA Volumes in Mathematics and its Applications*, Springer, pp. 95–101.

[27]Kesten, H., Ney, P. and Spitzer, F. (1966) The Galton–Watson process with mean one and finite variance. Teor. Verojatnost. i Primenen. 11 579–611.

[28]Kolchin, V. F. (1986) Random Mappings, Translation Series in Mathematics and Engineering, Optimization Software Inc.

[29]Kozma, G. and Nachmias, A. (2009) The Alexander–Orbach conjecture holds in high dimensions. Inventiones Math. 178 635–654.

[30]Kozma, G. and Nachmias, A. A note about critical percolation on finite graphs. *J. Theoret. Probab*., to appear.

[31]Levin, D. A., Peres, Y. and Wilmer, E. L. (2009) Markov Chains and Mixing Times, AMS.

[32]Łuczak, T. (1990) Component behavior near the critical point of the random graph process. Random Struct. Alg. 1 287–310.

[33]Luczak, M. and Winkler, P. (2004) Building uniformly random subtrees. Random Struct. Alg. 24 420–443.

[35]Matthews, P. (1988) Covering problems for Markov chains. Ann. Probab. 16 1215–1228.

[36]Mihail, M. and Papadimitriou, C. H. (1994) On the random walk method for protocol testing. In Computer Aided Verification (Stanford 1994), Vol. 818 of *Lecture Notes in Computer Science*, Springer, pp. 132–141.

[37]Nachmias, A. (2009) Mean-field conditions for percolation on finite graphs. Geometric Funct. Anal. 19 1171–1194.

[38]Nachmias, A. and Peres, Y. (2008) Critical random graphs: Diameter and mixing time. Ann. Probab. 36 1267–1286.

[39]Nachmias, A. and Peres, Y. Critical percolation on random regular graphs. *Random Struct. Alg*., to appear.

[40]Nash-Williams, C.St, J. A. (1959) Random walk and electric currents in networks. Proc. Cambridge Philos. Soc. 55 181–194.

[41]Pittel, B. (2008) Edge percolation on a random regular graph of low degree. Ann. Probab. 36 1359–1389.

[42]Stroock, D. W. and Varadhan, S. R. S. (1979) Multidimensional Diffusion Processes, Vol. 233 of *Grundlehren der Mathematischen Wissenschaften*, Springer.

[43]Talagrand, M. (2005) The Generic Chaining: Upper and Lower Bounds of Stochastic Processes, Springer Monographs in Mathematics, Springer.

[44]Tetali, P. (1991) Random walks and the effective resistance of networks. J. Theoret. Probab. 4 101–109.

[45]Winkler, P. and Zuckerman, D. (1996) Multiple cover time. Random Struct. Alg. 9 403–411.