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

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 Various variants of Hamiltonian problems

2018 ◽  
Author(s):  
Thinh D. Nguyen
Keyword(s):  
Hamiltonian Cycle ◽  
Short Note ◽  
Hamiltonian Path ◽  
Hamiltonian Problems ◽  
Hard Problems ◽  
Hamiltonian Path Problems ◽  
Mathematics Community

Hamiltonian cycle and Hamiltonian path problems are famous hard problems. The Hamiltonian cycle seems to have received more attention from the mathematics community. In this short note, we want to mitigate this bias a little bit. Keeping on track with the Prasolov and Sharygin kinds of doing mathematics, we give several simple constructions to show the hardness of some variants of Hamiltonian path problems.

A Parallel Reduction of Hamiltonian Cycle to Hamiltonian Path in Tournaments

1995 ◽  
Vol 19 (3) ◽  
pp. 432-440 ◽  
Author(s):  
E. Bampis ◽  
M. Elhaddad ◽  
Y. Manoussakis ◽  
M. Santha
Keyword(s):  
Hamiltonian Cycle ◽  
Hamiltonian Path ◽  
Parallel Reduction

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.

scholarly journals Maximum graphs non-Hamiltonian-connected from a vertex

1984 ◽  
Vol 25 (1) ◽  
pp. 97-98
Author(s):  
G. R. T. Hendry
Keyword(s):  
Hamiltonian Cycle ◽  
Hamiltonian Path ◽  
Hamiltonian Graphs ◽  
Connected Graphs ◽  
Hamiltonian Connected

A path (cycle) in a graph G is called a hamiltonian path (cycle) of G if it contains every vertex of G. A graph is hamiltonian if it contains a hamiltonian cycle. A graph G is hamiltonian-connectedif it contains a u-vhamiltonian path for each pair u, v of distinct vertices of G. A graph G is hamiltonian-connected from a vertex v of G if G contains a v-whamiltonian path for each vertex w≠v. Considering only graphs of order at least 3, the class of graphs hamiltonian-connected from a vertex properly contains the class of hamiltonian-connected graphs and is properly contained in the class of hamiltonian graphs.

scholarly journals Hamiltonian Cycle in K1,r-Free Split Graphs — A Dichotomy

2021 ◽  
pp. 1-32
Author(s):  
P. Renjith ◽  
N. Sadagopan
Keyword(s):  
Polynomial Time ◽  
Maximum Degree ◽  
Optimization Problem ◽  
Hamiltonian Cycle ◽  
Hamiltonian Path ◽  
Np Hard ◽  
Polynomial Time Algorithms ◽  
Split Graphs ◽  
Np Complete ◽  
Cycle Path

For an optimization problem known to be NP-Hard, the dichotomy study investigates the reduction instances to determine the line separating polynomial-time solvable vs NP-Hard instances (easy vs hard instances). In this paper, we investigate the well-studied Hamiltonian cycle problem (HCYCLE), and present an interesting dichotomy result on split graphs. T. Akiyama et al. (1980) have shown that HCYCLE is NP-complete on planar bipartite graphs with maximum degree [Formula: see text]. We use this result to show that HCYCLE is NP-complete for [Formula: see text]-free split graphs. Further, we present polynomial-time algorithms for Hamiltonian cycle in [Formula: see text]-free and [Formula: see text]-free split graphs. We believe that the structural results presented in this paper can be used to show similar dichotomy result for Hamiltonian path problem and other variants of Hamiltonian cycle (path) problems.

scholarly journals Hamiltonian paths in odd graphs

2009 ◽  
Vol 3 (2) ◽  
pp. 386-394 ◽  
Author(s):  
Letícia Bueno ◽  
Luerbio Faria ◽  
Figueiredo De ◽  
Fonseca Da
Keyword(s):  
Hamiltonian Cycle ◽  
Hamiltonian Path ◽  
Transitive Graph ◽  
Direct Computation ◽  
Hamiltonian Paths ◽  
Vertex Transitive ◽  
Vertex Transitive Graphs ◽  
Vertex Transitive Graph ◽  
Transitive Graphs ◽  
Connected Vertex

Lov?sz conjectured that every connected vertex-transitive graph has a Hamiltonian path. The odd graphs Ok form a well-studied family of connected, k-regular, vertex-transitive graphs. It was previously known that Ok has Hamiltonian paths for k ? 14. A direct computation of Hamiltonian paths in Ok is not feasible for large values of k, because Ok has (2k - 1, k - 1) vertices and k/2 (2k - 1, k - 1) edges. We show that Ok has Hamiltonian paths for 15 ? k ? 18. Instead of directly running any heuristics, we use existing results on the middle levels problem, therefore further relating these two fundamental problems, namely finding a Hamiltonian path in the odd graph and finding a Hamiltonian cycle in the corresponding middle levels graph. We show that further improved results for the middle levels problem can be used to find Hamiltonian paths in Ok for larger values of k.

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