A note on ‘Modified Hamiltonian chain: a graph theoretic approach to group technology’ after S. K. Mukhopadhyay, K. Ramesh Babu and K. V. Vijai Sai

A k-Partition, Graph Theoretic Approach to Perceptual Organization

This paper presents an k-partition, graph theoretic approach to perceptual organization. Principal results include a generalization of the bi-partition normalized cut to a k-partition measure, and a derivation of a sub-optimal, polynomial time solution to the NP-hard k-partition problem. The solution is obtained by first relaxing to an eigenvalue problem, followed by a heuristic procedure to en...

A K-Theoritic Approach to Some C*-Algebras

In this paper we look at the K-theory of a specific C*-algebra closely related to the irrational rotation algebra. Also it is shown that any automorphism of a C*-algebra A induces group automorphisms of K_{1}(A) amd K_{0}(A) in an obvious way. An interesting problem for any C*-algebra A is to find out whether, given an automorphism of K_{0}(A) and an automorphism of K_{1}(A), we can lift them t...

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A Note on Random k-SAT for Moderately Growing k

Consider a random instance I of k-SAT with n variables and m clauses. Suppose that θ, c > 0 are any fixed real numbers. Let k = k(n) ≥ ( 1 2 + θ ) log2 n. We prove that lim n→∞ Pr(I is satifiable) = { 1 m ≤ ( 1− c √ n ) 2kn ln 2 0 m ≥ ( 1 + c √ n ) 2kn ln 2.

A [k, k+1]-Factor Containing A Given Hamiltonian Cycle

We prove the following best possible result. Let k ≥ 2 be an integer and G be a graph of order n with minimum degree at least k. Assume n ≥ 8k− 16 for even n and n ≥ 6k−13 for odd n. If the degree sum of each pair of nonadjacent vertices of G is at least n, then for any given Hamiltonian cycle C of G, G has a [k, k + 1]-factor containing C. Submitted: December 15, 1997; Accepted: November 27, 1...