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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.

- Xingxing Yu
- 1997

We study the existence of certain disjoint paths in planar graphs and generalize a theorem of Thomassen on planarizing cycles in surfaces. Results are used to prove that every 5-connected triangulation of a surface with sufficiently large representativity is hamiltonian, thus verifying a conjecture of Thomassen. We also obtain results about spanning walks… (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)

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 class of graphs with no K3,t-minors, t ≥ 3, contains all planar graphs and plays an important role in graph minor theory. In 1992, Seymour and Thomas conjectured the existence of a function α(t) > 0 and a constant β > 0, such that every 3-connected n-vertex graph with no K 3,t-minors, t ≥ 3, contains a cycle of length at least α(t)n β. The purpose of… (More)

- Serguei Norine, Richard Duke, William T. Trotter, Xingxing Yu, Maria Chudnovsky, Matt DeVos +10 others
- 2005