Star-critical Ramsey number of large cycle and book of different orders

2021 ◽  
Author(s):  
Yan Li ◽  
Yusheng Li ◽  
Ye Wang
Keyword(s):  
Ramsey Number ◽  
Large Cycle

Study on the "Phase Hopping" AC-AC Frequency Conversion Method with Approximately Continuous Frequencies

2020 ◽  
Vol 13 (8) ◽  
pp. 1217-1226
Author(s):  
Zhengwang Xu ◽  
Guozhuang Jiang ◽  
Ke Kun ◽  
Yuchun Yi
Keyword(s):  
Output Voltage ◽  
Frequency Conversion ◽  
Frequency Control ◽  
Actual Application ◽  
Power Frequency ◽  
Voltage Frequency ◽  
The Law ◽  
Large Cycle ◽  
Selection Of ◽  
Conversion Technology

Background: The output voltage frequency for the previously proposed "phase hopping" AC-AC frequency conversion technology is determined by the law that the number of output voltage cycles is reduced by one relative to the power frequency in a large cycle containing six jumps. According to the law, only a limited number of output frequencies, such as 37.5 Hz, 42.86 Hz and 45 Hz are found. Due to the large spacing between the output frequencies, the "phase hopping" frequency conversion technology is difficult to put into practical use. Methods: In this paper, the law of the output frequency control is generalized so that the number of output cycles in a large cycle is reduced by n relative to the power frequency. The analysis shows that the appropriate selection of large cycles, including the number of power frequency cycles and the value of n, can find more frequencies to be used. Reducing the interval between the output frequencies within 1Hz. Results: The analysis results were verified in simulation by MATLAB, and the harmonics and the feasibility of the actual application were analyzed. Conclusion: Finally, an experimental platform was built and an experimental analysis was carried out. The experimental results show that the theoretical and simulation analyses are correct.

scholarly journals A Note on On-Line Ramsey Numbers for Some Paths

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 735
Author(s):  
Tomasz Dzido ◽  
Renata Zakrzewska
Keyword(s):  
Ramsey Number ◽  
Ramsey Numbers ◽  
Minimum Number ◽  
On Line ◽  
Infinite Set ◽  
Do So

We consider the important generalisation of Ramsey numbers, namely on-line Ramsey numbers. It is easiest to understand them by considering a game between two players, a Builder and Painter, on an infinite set of vertices. In each round, the Builder joins two non-adjacent vertices with an edge, and the Painter colors the edge red or blue. An on-line Ramsey number r˜(G,H) is the minimum number of rounds it takes the Builder to force the Painter to create a red copy of graph G or a blue copy of graph H, assuming that both the Builder and Painter play perfectly. The Painter’s goal is to resist to do so for as long as possible. In this paper, we consider the case where G is a path P4 and H is a path P10 or P11.

scholarly journals New values for the bipartite Ramsey number of the four-cycle versus stars

2021 ◽  
Vol 344 (5) ◽  
pp. 112320
Author(s):  
Imre Hatala ◽  
Tamás Héger ◽  
Sam Mattheus
Keyword(s):  
Ramsey Number

scholarly journals On the size Ramsey number of all cycles versus a path

2021 ◽  
Vol 344 (5) ◽  
pp. 112322
Author(s):  
Deepak Bal ◽  
Ely Schudrich
Keyword(s):  
Ramsey Number

scholarly journals Restricted size Ramsey number for 2K 2 versus disconnected graphs of order six

2021 ◽  
Vol 1722 ◽  
pp. 012048
Author(s):  
E Safitri ◽  
P John ◽  
D R Silaban
Keyword(s):  
Ramsey Number ◽  
Disconnected Graphs

scholarly journals Ramsey Numbers for Theta Graphs

2011 ◽  
Vol 2011 ◽  
pp. 1-9
Author(s):  
M. M. M. Jaradat ◽  
M. S. A. Bataineh ◽  
S. M. E. Radaideh
Keyword(s):  
Complete Graph ◽  
Ramsey Number ◽  
Ramsey Numbers ◽  
Subgraph Isomorphic

The graph Ramsey number is the smallest integer with the property that any complete graph of at least vertices whose edges are colored with two colors (say, red and blue) contains either a subgraph isomorphic to all of whose edges are red or a subgraph isomorphic to all of whose edges are blue. In this paper, we consider the Ramsey numbers for theta graphs. We determine , for . More specifically, we establish that for . Furthermore, we determine for . In fact, we establish that if is even, if is odd.

scholarly journals The Size, Multipartite Ramsey Numbers for nK2 Versus Path–Path and Cycle

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 764
Author(s):  
Yaser Rowshan ◽  
Mostafa Gholami ◽  
Stanford Shateyi
Keyword(s):  
Positive Integer ◽  
Ramsey Number ◽  
Complete Multipartite Graph ◽  
Ramsey Numbers ◽  
Multipartite Graph ◽  
Complete Multipartite ◽  
Monochromatic Copy

For given graphs G1,G2,…,Gn and any integer j, the size of the multipartite Ramsey number mj(G1,G2,…,Gn) is the smallest positive integer t such that any n-coloring of the edges of Kj×t contains a monochromatic copy of Gi in color i for some i, 1≤i≤n, where Kj×t denotes the complete multipartite graph having j classes with t vertices per each class. In this paper, we computed the size of the multipartite Ramsey numbers mj(K1,2,P4,nK2) for any j,n≥2 and mj(nK2,C7), for any j≤4 and n≥2.

Mixed Ramsey Numbers Revisited

2003 ◽  
Vol 12 (5-6) ◽  
pp. 653-660
Author(s):  
C. C. Rousseau ◽  
S. E. Speed
Keyword(s):  
Asymptotic Behaviour ◽  
Ramsey Number ◽  
Open Problems ◽  
Free Graph ◽  
Ramsey Numbers ◽  
Dense Graphs

Given a graph Hwith no isolates, the (generalized) mixed Ramsey number is the smallest integer r such that every H-free graph of order r contains an m-element irredundant set. We consider some questions concerning the asymptotic behaviour of this number (i) with H fixed and , (ii) with m fixed and a sequence of dense graphs, in particular for the sequence . Open problems are mentioned throughout the paper.

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