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Ramsey numbers of stars versus wheels of similar sizes

2005
*
Discrete Mathematics
*

We study the

doi:10.1016/j.disc.2004.12.003
fatcat:22vkfi5ymbdixbeemy5mzw2jz4
*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. ...##
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Small Ramsey Numbers

2011
*
Electronic Journal of Combinatorics
*

We do not attempt complete coverage

doi:10.37236/21
fatcat:xsh3n7wd2fbibgxla3okg5dfxq
*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 ...##
###
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)). ...##
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Star-critical Ramsey numbers

2011
*
Discrete Applied Mathematics
*

We find the

doi:10.1016/j.dam.2010.11.007
fatcat:w2gt7xzegjdcvlx7ffu24r2kca
*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. ...##
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On the union of graphs Ramsey numbers

2014
*
Applied Mathematical Sciences
*

Let H be a graph with the chromatic

doi:10.12988/ams.2014.311641
fatcat:eve7zny6lzgd3jay4dex3pi5za
*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 . ...##
###
A theorem on cycle–wheel Ramsey number

2012
*
Discrete Mathematics
*

For two given graphs G 1 and G 2 , the

doi:10.1016/j.disc.2011.11.022
fatcat:puyjdqnwgbffjeyjv7j5go3pha
*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. ...##
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Ramsey numbers of long cycles versus books or wheels

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. ...

##
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Master index to volumes 291-300

2005
*
Discrete Mathematics
*

., A new formula for an evaluation

doi:10.1016/s0012-365x(05)00445-0
fatcat:b5va3kwxz5fufkugwpvscg7oea
*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. ...##
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Recent developments in graph Ramsey theory
[article]

2015
*
arXiv
*
pre-print

Given a graph H, the

arXiv:1501.02474v3
fatcat:q3qcowfhgjbp5j36oetad6qdnq
*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. ...##
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Structural realism versus deployment realism: A comparative evaluation

2016
*
Studies in History and Philosophy of Science Part A
*

I discuss a set

doi:10.1016/j.shpsa.2016.06.006
pmid:27692219
fatcat:3iqb5btacnhrfhafo7b4rz4rei
*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. ...##
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The Imaging X-Ray Polarimetry Explorer (IXPE): Pre-Launch
[article]

2021
*
arXiv
*
pre-print

During its 2-year baseline mission, IXPE will conduct precise polarimetry for samples

arXiv:2112.01269v2
fatcat:2ovbhefna5a5nap3feconjswey
*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. ...##
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On the path-avoidance vertex-coloring game

2011
*
Electronic Notes in Discrete Mathematics
*

For a large class

doi:10.1016/j.endm.2011.10.010
fatcat:g43e67c2z5dabeejz6ifqtjlfq
*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). ...##
###
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 ...

##
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GRIS: The grating infrared spectrometer

1994
*
Publications of the Astronomical Society of the Pacific
*

An echelle grating, ruled on both sides, provides resolutions

doi:10.1086/133348
fatcat:4b7gsmw42fexzines6ou65oq5m
*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. ...##
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New Techniques

1993
*
International Astronomical Union Colloquium
*

AbstractRoutine millimagnitude photometry may require a new approach to reduction

doi:10.1017/s025292110000748x
fatcat:s3mows2fhrhgtinenvvizafbs4
*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. ...
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