1 A graph G is hamiltonian-connected if any two of its vertices are connected by a Hamilton 2 path (a path including every vertex of G); and G is s-hamiltonian-connected if the deletion 3 of any vertex subset with at most s vertices results in a hamiltonian-connected graph. In this 4 paper, we prove that the line graph of a (t+4)-edge-connected graph is (t+2)-hamiltonian5 connected if and only ...

We describe fault tolerant routing of multi cast messages in mesh based wormhole switched multicom puters With the proposed techniques multiple convex faults can be tolerated The fault information is kept locally each fault free processor needs to know the status of the links incident on it only Furthermore the proposed tech niques are deadlock and livelock free and guarantee deliv ery of messa...

We describe fault-tolerant routing of multi-cast messages in mesh-based wormhole-switched multicom-puters. With the proposed techniques, multiple convex faults can be tolerated. The fault information is kept locally| each fault-free processor needs to know the status of the links incident on it only. Furthermore, the proposed techniques are deadlock-and livelock-free and guarantee delivery of m...

A block-chain is a graph whose block graph is a path, i.e. it is either a P1, a P2, or a 2-connected graph, or a graph of connectivity 1 with exactly two end-blocks. A graph is called traceable if it contains a Hamilton path. A traceable graph is clearly a block-chain, but the reverse does not hold in general. In this paper we characterize all pairs of connected graphs {R, S} such that every {R...

Recently, Wellner et al. [Proc. Natl. Acad. Sci. U.S.A. 99, 8015 (2002)]] proposed a principle for predicting a stable scroll wave filament shape as a geodesic in a 3D space with a metric determined by the inverse diffusivity tensor of the medium. Using the Hamilton-Jacobi theory we show that this geodesic is the shortest path for a wave propagating through the medium. This allows the use of sh...

A weighted graph is one in which every edge e is assigned a nonnegative number w(e), called the weight of e. For a vertex v of a weighted graph, d(v) is the sum of the weights of the edges incident to v. And the weight of a path is the sum of the weights of the edges belonging to it. In this paper, we give a sufficient condition for a weighted graph to have a heavy path which joins two specifie...

we present a matching and lp based heuristic algorithm that decides graph non-hamiltonicity. each of the n! hamilton cycles in a complete directed graph on n + 1 vertices corresponds with each of the n! n-permutation matrices p, such that pu,i = 1 if and only if the ith arc in a cycle enters vertex u, starting and ending at vertex n + 1. a graph instance (g) is initially coded as exclusion set ...

The semi-classical approximation to black hole partition functions is not welldefined, because the classical action is unbounded and the first variation of the uncorrected action does not vanish for all variations preserving the boundary conditions. Both problems can be solved by adding a Hamilton-Jacobi counterterm. I show that the same problem and solution arises in quantum mechanics for half...

Let n = 2k + 1 with 0 < k ∈ Z and let Mk be the subgraph induced by the kand (k + 1)-levels of the n-cube graph. A system of numeration according to which the nonnegative integers are written as restricted growth strings, so called by Arndt and Ruskey, has specifically the k-th Catalan number Ck = (n k ) /n expressed as 10k. This permits a linear ordering of the vertex set of a quotient graph R...