New sufficient conditions for Hamiltonian paths

Rahman, M. Sohel; Kaykobad, M.; Firoz, Jesun Sahariar

doi:10.1109/iccitechn.2012.6509716

Cited by 3 publications

(3 citation statements)

References 10 publications

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“…Connections exist only between infills that do not belong to the same sub-polygon (cluster) and are assigned with weights. The Hamiltonian search is basically NP-hard [35]. In the graphs presented, the computation of a Hamiltonian path would take a significant amount of time.…”

Section: Meta Path Searchmentioning

confidence: 99%

A Robot-Centered Path-Planning Algorithm for Multidirectional Additive Manufacturing for WAAM Processes and Pure Object Manipulation

et al. 2021

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Previous algorithms for slicing, path planning or trajectory planning of additive manufacturing cannot be used consistently for multidirectional additive manufacturing with pure object manipulation in wire-arc additive manufacturing. This work presents a novel path planning approach that directly takes robot kinematics into account and thus ensures the reachability of all critical path poses. In an additional step, the planned path segments are smoothed so that joint velocity limits are respected. It is shown that the implemented path planner generates executable robot paths and at the same time maintains the process quality (in this case, sufficient coverage of the slice area). While the introduced method enables the generation of reachable printing paths, the smoothing algorithm allows for the execution of the path with respect to the robot’s velocity limits and at the same time improves the slice coverage. Future experiments will show the realization of the real robot setup presented.

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Section: Meta Path Searchmentioning

confidence: 99%

A Robot-Centered Path-Planning Algorithm for Multidirectional Additive Manufacturing for WAAM Processes and Pure Object Manipulation

et al. 2021

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“…Dudek et al ( 2012 ) studied the existence of properly colored and rainbow Hamilton cycles in colored k-uniform complete hypergraphs, . Rahman et al ( 2014 ) presented a new degree based sufficient conditions for the existence of Hamiltonian paths in a graph. In 2015, Dudek and Ferrara ( 2015 ) revised the results proved by Dudek, Frieze, and Rucinski (2012) and showed that there is a constant such that every —bounded edge—colored contains a properly colored overlapping Hamilton cycle.…”

Section: Related Workmentioning

confidence: 99%

A new algorithm to find fuzzy Hamilton cycle in a fuzzy network using adjacency matrix and minimum vertex degree

Gani¹,

Latha²

2016

SpringerPlus

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A Hamiltonian cycle in a graph is a cycle that visits each node/vertex exactly once. A graph containing a Hamiltonian cycle is called a Hamiltonian graph. There have been several researches to find the number of Hamiltonian cycles of a Hamilton graph. As the number of vertices and edges grow, it becomes very difficult to keep track of all the different ways through which the vertices are connected. Hence, analysis of large graphs can be efficiently done with the assistance of a computer system that interprets graphs as matrices. And, of course, a good and well written algorithm will expedite the analysis even faster. The most convenient way to quickly test whether there is an edge between two vertices is to represent graphs using adjacent matrices. In this paper, a new algorithm is proposed to find fuzzy Hamiltonian cycle using adjacency matrix and the degree of the vertices of a fuzzy graph. A fuzzy graph structure is also modeled to illustrate the proposed algorithms with the selected air network of Indigo airlines.

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“…Although, Hamilton solved this particular puzzle, evaluation Hamiltonian cycles or paths in arbitrary graphs are proved expected among the hardest problems of information retrieval [1,2]. As a result, instead of complete characterization, most researchers aimed to find sufficient conditions for a graph to process a Hamiltonian cycle or path.…”

Section: Introductionmentioning

confidence: 99%

Sufficient Condition and Algorithm for Hamiltonian in 3-Connected 3-Regular Planar Bipartite Graph

Khaliluzzaman¹,

Islam²,

Hasan³

2015

IJCA

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A graph G (V, E) is said to be Hamiltonian if it contains a spanning cycle. The spanning cycle is called a Hamiltonian cycle of G and G is said to be a Hamiltonian graph. A Hamiltonian path is a path that contains all the vertices in V (G) but does not return to the vertex in which it began. In this paper, we study Hamiltonicity of 3-connected, 3-regular planar bipartite graph G with partite sets V=M  N. We shall prove that G has a Hamiltonian cycle if G is balanced with M = N. For that we present an algorithm for a bipartite graph K M,N where M>3, N>3 and M,N both are even to possess a Hamiltonian cycle. In particular, we also prove a theorem for S proper subset (M or N) of V the number of components W (G-S) = S implies the graph has a Hamiltonian path.

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New sufficient conditions for Hamiltonian paths

Abstract: A Hamiltonian path in a graph is a path involving all the vertices of the graph. In this paper, we revisit the famous Hamiltonian path problem and present new sufficient conditions for the existence of a Hamiltonian path in a graph.

Cited by 3 publications

References 10 publications

A Robot-Centered Path-Planning Algorithm for Multidirectional Additive Manufacturing for WAAM Processes and Pure Object Manipulation

A Robot-Centered Path-Planning Algorithm for Multidirectional Additive Manufacturing for WAAM Processes and Pure Object Manipulation

A new algorithm to find fuzzy Hamilton cycle in a fuzzy network using adjacency matrix and minimum vertex degree

Sufficient Condition and Algorithm for Hamiltonian in 3-Connected 3-Regular Planar Bipartite Graph

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