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Ramsey numbers of stars versus wheels of similar sizes

Aleksandra Korolova
2005 Discrete Mathematics  
We study the Ramsey number R(W m , S n ) for a star S n on n vertices and a wheel W m on m + 1 vertices.  ...  We show that the Ramsey number R(W m , S n ) = 3n − 2 for n = m, m + 1, and m + 2, where m 7 and odd.  ...  Acknowledgements This research was performed under the supervision of Prof. Joseph Gallian at the University of Minnesota Duluth. The work was supported by NSF Grant DMS-0137611.  ... 
doi:10.1016/j.disc.2004.12.003 fatcat:22vkfi5ymbdixbeemy5mzw2jz4

Small Ramsey Numbers

Stanisław Radziszowski
2011 Electronic Journal of Combinatorics  
We do not attempt complete coverage of asymptotic behavior of Ramsey numbers, but concentrate on their specific values.  ...  We present data which, to the best of our knowledge, includes all known nontrivial values and bounds for specific graph, hypergraph and multicolor Ramsey numbers, where the avoided graphs are complete  ...  completed [LiNing2] Wheels versus fans and wheels [ZhaBC4] Wheels versus some trees [RaeZ, ZhuZL] Wheels versus books [Zhou3] Wheels versus unions of stars [BaHA, HaBA2, SuBAU1] Wheels versus linear  ... 
doi:10.37236/21 fatcat:xsh3n7wd2fbibgxla3okg5dfxq

Page 8947 of Mathematical Reviews Vol. , Issue 2003m [page]

2003 Mathematical Reviews  
Schelp (1-MEMP; Memphis, TN) 2003m:05130 05C55 05C15 Pikhurko, Oleg (4-CAMB; Cambridge) Size Ramsey numbers of stars versus 4-chromatic graphs. (English summary) J.  ...  The size Ramsey number /F(F, Fy) is the minimum number of edges in a graph G such that G — (F\, F)).  ... 

Star-critical Ramsey numbers

Jonelle Hook, Garth Isaak
2011 Discrete Applied Mathematics  
We find the star-critical Ramsey number for trees versus complete graphs, multiple copies of K 2 and K 3 , and paths versus a 4-cycle.  ...  Thus, we introduce the star-critical Ramsey number r * (G, H) as the smallest integer k such that every 2-coloring of the edges of K r − K 1,r−1−k contains either a red copy of G or a blue copy of H.  ...  In addition, the authors would like to thank Doug West and an anonymous referee for the terminology suggestions of star-critical Ramsey number and (G, H)-free coloring, respectively.  ... 
doi:10.1016/j.dam.2010.11.007 fatcat:w2gt7xzegjdcvlx7ffu24r2kca

On the union of graphs Ramsey numbers

I Wayan Sudarsana, Edy Tri Baskoro, Hilda Assiyatun, Saladin Uttunggadewa
2014 Applied Mathematical Sciences  
Let H be a graph with the chromatic number χ(H) and the chromatic surplus σ(H). A connected graph G of order n is called good with respect to H,  ...  The following theorem deals with the Ramsey number for a union of graphs containing no H-good components. In particular, a union of stars with different sizes versus wheel of order seven.  ...  We denote a path on n vertices by P n , a star on n vertices by S n , a cycle on n vertices by C n , a complete graph on n vertices by K n , and a wheel on n + 1 vertices by W n .  ... 
doi:10.12988/ams.2014.311641 fatcat:eve7zny6lzgd3jay4dex3pi5za

A theorem on cycle–wheel Ramsey number

Yaojun Chen, T.C. Edwin Cheng, C.T. Ng, Yunqing Zhang
2012 Discrete Mathematics  
For two given graphs G 1 and G 2 , the Ramsey number R(G 1 , G 2 ) is the smallest integer N such that for any graph G of order N, either G contains G 1 or the complement of G contains G 2 .  ...  Let C n denote a cycle of order n and W m a wheel of order m + 1.  ...  Acknowledgments We are grateful to the referees for their careful comments on our earlier version of this paper.  ... 
doi:10.1016/j.disc.2011.11.022 fatcat:puyjdqnwgbffjeyjv7j5go3pha

Ramsey numbers of long cycles versus books or wheels

Lingsheng Shi
2010 European journal of combinatorics (Print)  
number of a book B m = K 2 * K c m versus a cycle C n of order n satisfies R(B m , C n ) = 2n − 1 for n > (6m + 7)/4 which improves a result of Faudree et al., and the Ramsey number of a cycle C n versus  ...  As consequences, Ramsey numbers of other sparse graphs are also obtained.  ...  Acknowledgements The author thanks Ralph Faudree for sending him an offprint [11] , Mihyun Kang for sending him the reference [3] , and a referee for simplifying the proof of Theorem 2.3.  ... 
doi:10.1016/j.ejc.2009.07.004 fatcat:fzdomgcvebazzgkeqenfufm3fy

Master index to volumes 291-300

2005 Discrete Mathematics  
., A new formula for an evaluation of the Tutte polynomial of a matroid 300 (2005) 235-238 Korolova, A., Ramsey numbers of stars versus wheels of similar sizes 292 (2005) 107-117 Kotlar, D. and R.  ...  Swanepoel, Ramsey degrees of bipartite graphs: M., H. Hatami and E.S. Mahmoodian, On the size of the minimum critical set of a Latin square 293 (2005) 121-127 Gibson, P.C., M. Pouzet and R.E.  ... 
doi:10.1016/s0012-365x(05)00445-0 fatcat:b5va3kwxz5fufkugwpvscg7oea

Recent developments in graph Ramsey theory [article]

David Conlon, Jacob Fox, Benny Sudakov
2015 arXiv   pre-print
Given a graph H, the Ramsey number r(H) is the smallest natural number N such that any two-colouring of the edges of K_N contains a monochromatic copy of H.  ...  Even so, there has been a great deal of recent progress on the study of Ramsey numbers and their variants, spurred on by the many advances across extremal combinatorics.  ...  The authors would like to thank the anonymous referee for a number of useful comments.  ... 
arXiv:1501.02474v3 fatcat:q3qcowfhgjbp5j36oetad6qdnq

Structural realism versus deployment realism: A comparative evaluation

Timothy D. Lyons
2016 Studies in History and Philosophy of Science Part A  
I discuss a set of cases from the history of celestial mechanics, including some of the most important successes in the history of science.  ...  Exploring the implications for structural realism, I show that the need to accommodate these cases forces our notion of "structure" toward a dramatic depletion of logical content, threatening to render  ...  And a number of the false deployed theoretical posits identified above will likewise pollute the terms included in the Ramsey sentence, bringing their falsity with them.  ... 
doi:10.1016/j.shpsa.2016.06.006 pmid:27692219 fatcat:3iqb5btacnhrfhafo7b4rz4rei

The Imaging X-Ray Polarimetry Explorer (IXPE): Pre-Launch [article]

Martin C. Weisskopf, Paolo Soffitta, Luca Baldini, Brian D. Ramsey, Stephen L. O'Dell, Roger W. Romani, Giorgio Matt, William D. Deininger, Wayne H. Baumgartner, Ronaldo Bellazzini, Enrico Costa, Jeffery J. Kolodziejczak (+146 others)
2021 arXiv   pre-print
During its 2-year baseline mission, IXPE will conduct precise polarimetry for samples of multiple categories of X-ray sources, with follow-on observations of selected targets.  ...  The mission will open a new window of investigation - imaging X-ray polarimetry.  ...  Modulation Factor The modulation amplitude is the fractional variation in the number of detected events versus position angle.  ... 
arXiv:2112.01269v2 fatcat:2ovbhefna5a5nap3feconjswey

On the path-avoidance vertex-coloring game

Torsten Mütze, Reto Spöhel
2011 Electronic Notes in Discrete Mathematics  
For a large class of graphs F , including cliques, cycles, complete bipartite graphs, hypercubes, wheels, and stars of arbitrary size, a simple greedy strategy is optimal for Painter and closed formulas  ...  This parameter was introduced in a recent paper [arXiv:1103.5849 ], where it was shown that the online vertex-Ramsey density determines the threshold of a similar probabilistic one-player game (Painter  ...  Lemma 9 (Tree versus star upper bound). For any tree F and any ≥ 1 we have k * (F, S ) ≤ v(F ) · v(S ) = v(F ) · ( + 1).  ... 
doi:10.1016/j.endm.2011.10.010 fatcat:g43e67c2z5dabeejz6ifqtjlfq

Subject Index Volumes 1–200

2001 Discrete Mathematics  
size of a complete arcs, 2574 a graph, 2034, 2259, 2557, 3882, 4003, 5060, 5937 a largest pseudosnake, 2269 a maximal antichain, 3738 size Ramsey number, 1539, 3651, 5120 sequence, 4458 skeletal  ...  , 5703 stars, 1204 stratum sizes, 4385 strong connectivity numbers, 4045 tailed column convex polyominoes, 5568, see also stapo test sets, 2915 trees, 5090 vectors, 1682 vertices, 1266, 5801  ...  , 38, 226, 363, , 1326 Rado, 38, 226, 363, , 1491 Rado, 38, 226, 363, , 1709 Rado, 38, 226, 363, , 1761 Rado, 38, 226, 363, , 1800 for stars, 1385 Ramsey number, 9, 57, 95, 127, 155, 156, 178, 249, 257  ... 
doi:10.1016/s0012-365x(00)00471-4 fatcat:znxg54q6ifgutnhzj3urcw455y

GRIS: The grating infrared spectrometer

Rodger I. Thompson, Harland W. Epps, Greg Winters, William Womack, Eric Mentzell
1994 Publications of the Astronomical Society of the Pacific  
An echelle grating, ruled on both sides, provides resolutions of 3449 and 9439 per slit width, respectively.  ...  Rotation of the grating achieves several functions: 1/2 pixel spectrum stepping for full Nyquist sampling, a change in the wavelength regions falling on the detector, and the means for changing grating  ...  The authors wish to acknowledge the superb efforts of Robert Miller in the matching of and design consultation on the GRIS parts and structures.  ... 
doi:10.1086/133348 fatcat:4b7gsmw42fexzines6ou65oq5m

New Techniques

Jaap Tinbergen
1993 International Astronomical Union Colloquium  
AbstractRoutine millimagnitude photometry may require a new approach to reduction of photometric errors.  ...  Such an approach is outlined in this paper; it stresses elimination of each error as close to its source as possible. The possibilities provided by modern technology are reviewed in this light.  ...  By methods similar to determining a pointing model of a telescope from measured apparent positions of standard stars, it should be possible to disentangle drifts in the several component systems.  ... 
doi:10.1017/s025292110000748x fatcat:s3mows2fhrhgtinenvvizafbs4
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