Winding indexes of Max. and Min. Hamiltonians in N-Gons

2017 ◽  
Vol 09 (05) ◽  
pp. 1750061
Author(s):  
Blanca Isabel Niel
Keyword(s):  
Hamiltonian Path ◽  
Hamiltonian Cycles ◽  
Arithmetic Algorithm ◽  
Hamiltonian Path Problems

The resolutions of the different Shortest and Longest Euclidean Hamiltonian Path Problems on the vertices of simple regular [Formula: see text]-Gons, by means of a geometric and arithmetic algorithm allow us to define winding indexes for Euclidean Hamiltonian cycles. New statements characterize orientation of non-necessarily regular Hamiltonian cycles on the [Formula: see text]th roots of the unity embedded in the plane and deal with the existence of reflective bistarred Hamiltonian tours on vertices of coupled [Formula: see text]-Gons.

Parallel algorithms for the hamiltonian cycle and hamiltonian path problems in semicomplete bipartite digraphs

Algorithmica ◽  
1997 ◽  
Vol 17 (1) ◽  
pp. 67-87 ◽  
Author(s):  
J. Bang-Jensen ◽  
M. El Haddad ◽  
Y. Manoussakis ◽  
T. M. Przytycka
Keyword(s):  
Parallel Algorithms ◽  
Hamiltonian Cycle ◽  
Hamiltonian Path ◽  
Hamiltonian Path Problems

MUTUALLY INDEPENDENT HAMILTONIAN PATHS AND CYCLES IN HYPERCUBES

2006 ◽  
Vol 07 (02) ◽  
pp. 235-255 ◽  
Author(s):  
CHAO-MING SUN ◽  
CHENG-KUAN LIN ◽  
HUA-MIN HUANG ◽  
LIH-HSING HSU
Keyword(s):  
Bipartite Graph ◽  
Hamiltonian Cycle ◽  
Hamiltonian Path ◽  
Hamiltonian Cycles ◽  
Hamiltonian Paths ◽  
Mutually Independent ◽  
Hamiltonian Laceability

Two hamiltonian paths P1 = 〈v1, v2, …, vn(G) 〉 and P2 = 〈 u1, u2, …, un(G) 〉 of G are independent if v1 = u1, vn(G) = un(G), and vi ≠ ui for 1 < i < n(G). A set of hamiltonian paths {P1, P2, …, Pk} of G are mutually independent if any two different hamiltonian paths in the set are independent. A bipartite graph G is hamiltonian laceable if there exists a hamiltonian path joining any two nodes from different partite sets. A bipartite graph is k-mutually independent hamiltonian laceable if there exist k-mutually independent hamiltonian paths between any two nodes from different partite sets. The mutually independent hamiltonian laceability of bipartite graph G, IHPL(G), is the maximum integer k such that G is k-mutually independent hamiltonian laceable. Let Qn be the n-dimensional hypercube. We prove that IHPL(Qn) = 1 if n ∈ {1,2,3}, and IHPL(Qn) = n - 1 if n ≥ 4. A hamiltonian cycle C of G is described as 〈 u1, u2, …, un(G), u1 〉 to emphasize the order of nodes in C. Thus, u1 is the beginning node and ui is the i-th node in C. Two hamiltonian cycles of G beginning at u, C1 = 〈 v1, v2, …, vn(G), v1 〉 and C2 = 〈 u1, u2, …, un(G), u1 〉, are independent if u = v1 = u1, and vi ≠ ui for 1 < i ≤ n(G). A set of hamiltonian cycles {C1, C2, …, Ck} of G are mutually independent if any two different hamiltonian cycles are independent. The mutually independent hamiltonianicity of graph G, IHC(G), is the maximum integer k such that for any node u of G there exist k-mutually independent hamiltonian cycles of G starting at u. We prove that IHC(Qn) = n - 1 if n ∈ {1,2,3} and IHC(Qn) = n if n ≥ 4.

Optimal Control of Mobile Agents for Monitoring of Points on a Network

2014 ◽  
Vol 11 (2) ◽  
pp. 2-6
Author(s):  
V. Sgurev ◽  
S. Drangajov
Keyword(s):  
Mobile Agents ◽  
Network Flow ◽  
Hamiltonian Path ◽  
Hamiltonian Cycles ◽  
Optimal Trajectories ◽  
Network Nodes ◽  
Np Complete ◽  
Network Flow Programming ◽  
Similar Class ◽  
Edge Decomposition

Abstract This paper concerns the problems of finding optimal trajectories between nodes on a network, which must be periodically surveyed, and probably serviced. It is shown, that such trajectories may be generated if optimal Hamiltonian cycles are used between the separate network nodes under inspection. It is known that the Hamiltonian path problem is NP-complete, but an edge decomposition of the network is proposed. This is performed by reducing in a particular way to network flow circulations. The requirements and the equations for describing such circulation are pointed out. Defining of the optimal circulations of the mobile agents is reduced to network flow programming problems. A numerical example is presented for solving a similar class of monitoring problems by mobile agents.

EVERY LONGEST HAMILTONIAN PATH IN EVEN n-GONS

2012 ◽  
Vol 04 (04) ◽  
pp. 1250057 ◽  
Author(s):  
BLANCA I. NIEL
Keyword(s):  
Traveling Salesman Problem ◽  
Hamiltonian Cycle ◽  
Hamiltonian Path ◽  
Traveling Salesman ◽  
Maximum Traveling Salesman Problem ◽  
Longest Path ◽  
Hamiltonian Path Problems ◽  
Planar Rotations

We single out every longest path of n-1 order that solves each of the [Formula: see text] Longest Euclidean Hamiltonian Path Problems on the even nth root of the unity, by means of a geometric and arithmetic procedure. This identification is done regardless of planar rotations and orientation. In addition, the uniqueness of the Euclidean Hamiltonian cycle that resolves the Maximum Traveling Salesman Problem is shown.

scholarly journals Universal Biochip Readout of Directed Hamiltonian Path Problems

2003 ◽  
pp. 168-181 ◽  
Author(s):  
David Harlan Wood ◽  
Catherine L. Taylor Clelland ◽  
Carter Bancroft
Keyword(s):  
Hamiltonian Path ◽  
Hamiltonian Path Problems

Hamiltonian Cycles in Products of Graphs

1975 ◽  
Vol 17 (5) ◽  
pp. 763-765 ◽  
Author(s):  
Joseph Zaks
Keyword(s):  
Bipartite Graph ◽  
Complete Graph ◽  
Hamiltonian Cycle ◽  
Complete Bipartite Graph ◽  
Hamiltonian Path ◽  
Hamiltonian Cycles ◽  
Vertex Set ◽  
Cycle Path

Let V(G) and E(G) denote the vertex set and the edge set of a graph G; let Kn denote the complete graph with n vertices and let Kn, m denote the complete bipartite graph on n and m vertices. A Hamiltonian cycle (Hamiltonian path, respectively) in a graph G is a cycle (path, respectively) in G that contains all the vertices of G.

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