An argument for Hamiltonicity

Quasi-Hamiltonicity: A Series of Necessary Conditions for a Digraph to Be Hamiltonian

We introduce new necessary conditions, k-quasi-hamiltonicity (0 k n ? 1), for a digraph of order n to be hamiltonian. Every (k + 1)-quasi-hamiltonian digraph is also k-quasi-hamiltonian; we construct digraphs which are k-quasi-hamiltonian, but not (k + 1)-quasi-hamiltonian. We design an algorithm that checks k-quasi-hamiltonicity of a given digraph with n vertices and m arcs in time O(nm k). We...

Deciding Graph non-Hamiltonicity via a Closure Algorithm

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 ...

Hamiltonian Maker-Breaker games on small graphs

We look at the unbiased Maker-Breaker Hamiltonicity game played on the edge set of a complete graph Kn, where Maker’s goal is to claim a Hamiltonian cycle. First, we prove that, independent of who starts, Maker can win the game for n = 8 and n = 9. Then we use an inductive argument to show that, independent of who starts, Maker can win the game if and only if n ≥ 8. This, in particular, resolve...

An Approach for Solving Fuzzy Fredholm Integro-Difference Equations with Mixed Argument

An ‎E‎ffective Numerical Technique for Solving Second Order Linear Two-Point Boundary Value Problems with Deviating Argument

Based on reproducing kernel theory, an effective numerical technique is proposed for solving second order linear two-point boundary value problems with deviating argument. In this method, reproducing kernels with Chebyshev polynomial form are used (C-RKM). The convergence and an error estimation of the method are discussed. The efficiency and the accuracy of the method is demonstrated on some n...