A Hamiltonian path (cycle) of a graph is a simple path (cycle) which visits each vertex of the graph exactly once. The Hamiltonian path (cycle) problem is to determine whether a graph contains a Hamiltonian path (cycle). A graph is called Hamiltonian connected if there exists a Hamiltonian path between any two distinct vertices. Supergrid graphs were first introduced by us and include grid grap...

ÐIn this paper, we present four efficient parallel algorithms for computing a nonequijoin, called range-join, of two relations on N-dimensional mesh-connected computers. Range-joins of relations R and S are an important generalization of conventional equijoins and band-joins and are solved by permutation-based approaches in all proposed algorithms. In general, after sorting all subsets of both ...

Let G be a graph and H be a subgraph of G. If G contains a hamiltonian cycle C such that E(C)∩E(H) is empty, we say that C is an H-avoiding hamiltonian cycle. Let F be any graph. If G contains an H-avoiding hamiltonian cycle for every subgraph H of G such that H ∼= F , then we say that G is F -avoiding hamiltonian. In this paper, we give minimum degree and degree-sum conditions which ensure tha...

This paper investigates a variant of the Hamiltonian Cycle (HC) problem, named the Parity Hamiltonian Cycle (PHC ) problem: The problem is to find a closed walk visiting each vertex odd number of times, instead of exactly once. We show that the PHC problem is in P even when a closed walk is allowed to use an edge at most z = 4 times, by considering a T -join, which is a generalization of matchi...

Given a graph G = (V, E), V(G) = V and E(G) = E denote the vertex set and the edge set of G, respectively. All graphs considered in this paper are undirected graphs. A simple path (or path for short) is a sequence of adjacent edges (v1, v2), (v2, v3), ..., (vm-2, vm-1), (vm-1, vm), written as 〈v1, v2, v3, ..., vm〉, in which all of the vertices v1, v2, v3, ..., vm are distinct except possibly v1...

We prove that every Hamiltonian graph with n vertices and m edges has cycles of at least √ 4 7(m − n) different lengths. The coefficient 4/7 cannot be increased above 1, since when m = n2/4 there are √ m − n + 1 cycle lengths in Kn/2,n/2. For general m and n there are examples having at most 2 ⌈

In 1990, Hendry conjectured that every Hamiltonian chordal graph is cycle extendible; that is, the vertices of any non-Hamiltonian cycle are contained in a cycle of length one greater. We disprove this conjecture by constructing counterexamples on n vertices for any n ≥ 15. Furthermore, we show that there exist counterexamples where the ratio of the length of a non-extendible cycle to the total...

Algorithm tests if a Hamiltonian cycle exists in directed graphs, if it is exists algorithm can show found Hamiltonian cycle. If you want to test an undirected graph, such a graph should be converted to the form of directed graph. Previously known algorithm solving Hamiltonian cycle problem brute-force search can’t handle relatively small graphs. Algorithm presented here is referred to simply a...