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— In this work, we study a fundamental tradeoff issue in designing distributed hash table (DHT) in peer-to-peer networks: the size of the routing table v.s. the network diameter. It was observed by Ratnasamy et al. that existing DHT schemes either (a) have a routing table of size Ç´ÐÓÓ ¾ Òµ and network diameter of Ç´ÐÓÓ ¾ Òµ, or (b) have a routing table of… (More)

We prove the result stated in the title (conjectured by Grünbaum), and a conjecture of Plum-mer that every graph which can be obtained from a 4–connected planar graph by deleting two vertices is Hamiltonian. The proofs are constructive and give rise to polynomial–time algorithms.

— A number of Distributed Hash Table (DHT)-based protocols have been proposed to address the issue of scalability in peer-to-peer networks. However, it remains an open question whether there exists a DHT scheme that can achieve the theoretical lower bound of on network diameter when the average routing table size at nodes is no more than¨©. In this paper,… (More)

Motivated by a multi-tree approach to the design of reliable communication protocols, Itai and Rodeh gave a linear time algorithm for finding two independent spanning trees in a 2-connected graph. Cheriyan and Maheshwari gave an O(|V | 2) algorithm for finding three independent spanning trees in a 3-connected graph. In this paper we present an O(|V | 3)… (More)

We prove that every edge in a 5-connected graph embedded in the torus is contained in a Hamilton cycle. Our proof is constructive and implies a polynomial time algorithm for finding a Hamilton cycle. 1997 Academic Press

A graph is subcubic if its maximum degree is at most 3. The bipartite density of a graph G is max{ε(H)/ε(G) : H is a bipartite subgraph of G}, where ε(H) and ε(G) denote the numbers of edges in H and G, respectively. It is an NP-hard problem to determine the bipartite density of any given triangle-free cubic graph. Bondy and Locke gave a polynomial time… (More)

The circumference of a graph is the length of its longest cycles. Results of Jackson, and Jackson and Wormald, imply that the circumference of a 3-connected cubic n-vertex graph is Ω(n 0.694), and the circumference of a 3-connected claw-free graph is Ω(n 0.121). We generalise and improve the first result by showing that every 3-edge-connected graph with m… (More)

Moon and Moser in 1963 conjectured that if G is a 3-connected planar graph on n vertices, then G contains a cycle of length at least Ω(n log 3 2). In this paper, this conjecture is proved. In addition, the same result is proved for 3-connected graphs embeddable in the pro-jective plane, or the torus, or the Klein bottle.