scholarly journals Cycle covers (III) – Compatible circuit decomposition and K5-transition minor

2019 ◽  
Vol 137 ◽  
pp. 25-54 ◽  
Author(s):  
Herbert Fleischner ◽  
Behrooz Bagheri Gh. ◽  
Cun-Quan Zhang ◽  
Zhang Zhang
Keyword(s):  
Circuit Decomposition ◽  
Cycle Covers

scholarly journals Approximating Maximum Weight Cycle Covers in Directed Graphs with Weights Zero and One

Algorithmica ◽  
2005 ◽  
Vol 42 (2) ◽  
pp. 121-139 ◽  
Author(s):  
Markus Bläser ◽  
Bodo Manthey
Keyword(s):  
Directed Graphs ◽  
Maximum Weight ◽  
Cycle Covers

scholarly journals Implementation of the quantum Fourier transform on a hybrid qubit–qutrit NMR quantum emulator

2015 ◽  
Vol 13 (07) ◽  
pp. 1550059 ◽  
Author(s):  
Shruti Dogra ◽  
Arvind Dorai ◽  
Kavita Dorai
Keyword(s):  
Fourier Transform ◽  
Quantum Algorithms ◽  
Quantum Computers ◽  
Quantum Fourier Transform ◽  
Specific Implementation ◽  
Circuit Decomposition

The quantum Fourier transform (QFT) is a key ingredient of several quantum algorithms and a qudit-specific implementation of the QFT is hence an important step toward the realization of qudit-based quantum computers. This work develops a circuit decomposition of the QFT for hybrid qudits based on generalized Hadamard and generalized controlled-phase gates, which can be implemented using selective rotations in NMR. We experimentally implement the hybrid qudit QFT on an NMR quantum emulator, which uses four qubits to emulate a single qutrit coupled to two qubits.

scholarly journals Short Cycle Covers of Graphs with at Most 77% Vertices of Degree Two

10.37236/9284 ◽  
2020 ◽  
Vol 27 (4) ◽  
Author(s):  
Anna Kompišová ◽  
Robert Lukot'ka
Keyword(s):  
Double Cover ◽  
Short Cycle ◽  
Cycle Cover ◽  
M 10 ◽  
Cycle Covers

Let $G$ be a bridgeless multigraph with $m$ edges and $n_2$ vertices of degree two and let $cc(G)$ be the length of its shortest cycle cover. It is known that if $cc(G) < 1.4m$ in bridgeless graphs with $n_2 \le m/10$, then the Cycle Double Cover Conjecture holds. Fan (2017)  proved that if $n_2 = 0$, then $cc(G) < 1.6258m$ and $cc(G) < 1.6148m$ provided that $G$ is loopless; morever, if $n_2 \le m/30$, then $cc(G) < 1.6467m$. We show that for a bridgeless multigraph with $m$ edges and $n_2$ vertices of degree two, $cc(G) < 1.6148m + 0.0741n_2$. Therefore, if $n_2=0$, then $cc(G) < 1.6148m$ even if $G$ has loops; if $n_2 \le m/30$, then $cc(G) < 1.6173m$; and if $n_2 \le m/10$, then $cc(G) < 1.6223|E(G)|$. Our improvement is obtained by randomizing Fan's construction.

scholarly journals 1-Factor and Cycle Covers of Cubic Graphs

2014 ◽  
Vol 78 (3) ◽  
pp. 195-206 ◽  
Author(s):  
Eckhard Steffen
Keyword(s):  
Cubic Graphs ◽  
Cycle Covers

Cubic Graphs with No Short Cycle Covers

2021 ◽  
Vol 35 (3) ◽  
pp. 2223-2233
Author(s):  
Edita Máčajová ◽  
Martin Škoviera
Keyword(s):  
Cubic Graphs ◽  
Short Cycle ◽  
Cycle Covers

Shortest cycle covers

2012 ◽  
pp. 163-188
Author(s):  
Cun-Quan Zhang
Keyword(s):  
Cycle Covers

Research on Intelligent Fault Diagnosis Technique of Complex Equipment

2014 ◽  
Vol 945-949 ◽  
pp. 1098-1101
Author(s):  
Rui Zhu ◽  
Ming Ji Huang ◽  
Guo Bao Ding ◽  
Shuai Jia
Keyword(s):  
Fault Diagnosis ◽  
Decision Tree ◽  
Intelligent Fault Diagnosis ◽  
Intelligent Diagnosis ◽  
Complex Equipment ◽  
Circuit Decomposition ◽  
Diagnosis Technique

Aiming at the actual demand of complex equipment fault diagnosis, this paper made the fault intelligent diagnosis technology of a certain type of equipment as research object, analyzed the characteristics of equipment and its faults, presented four strategy to solve the problem: Circuit-decomposition, the decision tree, confirm key component using FMECA and establish model by PSPICE.And proving it by actual circuit.

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