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Flows and colorings
Published in Joanna A. Ellis-Monaghan, Iain Moffatt, Handbook of the Tutte Polynomial and Related Topics, 2022
Delia Garijo, Andrew Goodall, Jaroslav Nešetřil
Jaeger [645] used the fact, due to Tutte and to C. Nash-Williams, that a 4-edge-connected graph has two edge-disjoint spanning trees in order to prove that every 4-edge-connected graph has a nowhere-zero 4-flow. As nowhere-zero 4-flows of a cubic graph correspond to proper edge 3-colorings, the 4-flow conjecture implies that every bridgeless cubic graph without a Petersen minor is 3-edge-colorable. The latter was another conjecture of Tutte. A proof was announced by N. Robertson, P. Seymour, and R. Thomas in [966], thereby giving a strengthening of the four color theorem, which is equivalent to the assertion that planar cubic graphs without a bridge are 3-edge-colorable.
Analysis and Design of Single Stage Bridgeless Cuk Converter for Current Harmonics Suppression Using Particle Swarm Optimization Technique
Published in Electric Power Components and Systems, 2019
Gajendran Marimuthu, Mallapu Gopinath Umamaheswari
The Bridgeless Cuk converter parameters are designed with the following specifications: Switching frequency fs= 50 kHz, Duty cycle d = 0.67, Supply voltage Vs = 60 V, Output voltage Vo = 120 V, Output resistance RL = 48 Ω, Output current IL= 2.5 A, Ripple in source side inductor current ΔiL1 = 2.36% of the input current, Ripple in the capacitor voltage ΔvC1 = 6% of the output voltage (Vo) and ripple in the output capacitor is considered to be ΔvCO = 0.006% of output voltage. The values of inductors L1, L2, L01, and L02, capacitors C1, C2, and CO are designed using Eqs. (13)–(19)
A novel single-phase AC–DC bridgeless boost converter for PFC application
Published in International Journal of Electronics Letters, 2018
To make this bridgeless boost PFC converter to operate in DCM over the whole line cycles, the operation conditions related to duty cycle during any switching cycle must meet: