**Equipartitions of graphs**.

D. Eppstein, J. Feigenbaum, and C.L. Li.

*Discrete Mathematics*91 (3): 239–248, 1991.Considers partitions of the vertices of a graph into equal subsets, with few pairs of subsets connected by edges. (Equivalently we view the graph as a subgraph of a product in which one factor is sparse.) A random graph construction shows that such a factorization does not always exist.

**The distribution of cycle lengths in graphical models for iterative decoding**.

X. Ge, D. Eppstein, and P. Smyth.

arXiv:cs.DM/9907002.

Tech. Rep. 99-10, ICS, UCI, 1999.

IEEE Int. Symp. Information Theory, Sorrento, Italy, 2000.

*IEEE Trans. Information Theory*47 (6): 2549–2553, 2001.We compute the expected numbers of short cycles of each length in certain classes of random graphs used for turbocodes, estimate the probability that there are no such short cycles involving a given vertex, and experimentally verify our estimates. The scarcity of short cycles may help explain the empirically observed accuracy of belief-propagation based error-correction algorithms. Note, the TR, conference, and journal versions of this paper have slightly different titles.

**Fast approximation of centrality**.

D. Eppstein and J. Wang.

arXiv:cs.DS/0009005.

*12th ACM-SIAM Symp. Discrete Algorithms,*Washington, 2001, pp. 228–229.

*J. Graph Algorithms & Applications*8 (1): 39–45, 2004.We use random sampling to quickly estimate, for each vertex in a graph, the average distance to all other vertices.

**A steady state model for graph power laws**.

D. Eppstein and J. Wang.

2nd Int. Worksh. Web Dynamics, Honolulu, 2002.

arXiv:cs.DM/0204001.We propose a random graph model that (empirically) appears to have a power law degree distribution. Unlike previous models, our model is based on a Markov process rather than incremental growth. We compare our model with others in its ability to predict web graph clustering behavior.

Graph Theory – Publications – David Eppstein – Theory Group – Inf. & Comp. Sci. – UC Irvine

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