1,189 research outputs found
THE ELECTRONIC JOURNAL OF COMBINATORICS (2014), DS1.14 References
and Computing 11. The results of 143 references depend on computer algorithms. The references are ordered alphabetically by the last name of the first author, and where multiple papers have the same first author they are ordered by the last name of the second author, etc. We preferred that all work by the same author be in consecutive positions. Unfortunately, this causes that some of the abbreviations are not in alphabetical order. For example, [BaRT] is earlier on the list than [BaLS]. We also wish to explain a possible confusion with respect to the order of parts and spelling of Chinese names. We put them without any abbreviations, often with the last name written first as is customary in original. Sometimes this is different from the citations in other sources. One can obtain all variations of writing any specific name by consulting the authors database of Mathematical Reviews a
Small Ramsey Numbers
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 or complete without one edge. Many results pertaining to other more studied cases are also presented. We give references to all cited bounds and values, as well as to previous similar compilations. We do not attempt complete coverage of asymptotic behavior of Ramsey numbers, but concentrate on their specific values
On Size Bipartite and Tripartite Ramsey Numbers for The Star Forest and Path on 3 Vertices
For simple graphs G and H the size multipartite Ramsey number mj(G,H) is the smallest natural number t such that any arbitrary red-blue coloring on the edges of Kjxt contains a red G or a blue H as a subgraph. We studied the size tripartite Ramsey numbers m3(G,H) where G=mK1,n and H=P3. In this paper, we generalize this result. We determine m3(G,H) where G is a star forest, namely a disjoint union of heterogeneous stars, and H=P3. Moreover, we also determine m2(G,H) for this pair of graphs G and H
Some exact values on Ramsey numbers related to fans
For two given graphs and , the Ramsey number is the smallest
integer such that any red-blue edge-coloring of the complete graph
contains a red or a blue . When , we simply write . For an
positive integer , let be a star with vertices, be a
fan with vertices consisting of triangles sharing one common vertex,
and be a graph with vertices obtained from the disjoint union of
triangles. In 1975, Burr, Erd\H{o}s and Spencer \cite{B} proved that
for . However, determining the exact value of
is notoriously difficult. So far, only has been proved. Notice
that both and contain triangles and for
all . Chen, Yu and Zhao (2021) speculated that for sufficiently large. In this paper, we first prove that
for , where if is
odd and if is even. Applying the exact values of
, we will confirm for by showing that
.Comment: 10 pages, 3 figure
The bipartite Ramsey numbers
For the given bipartite graphs , the multicolor bipartite
Ramsey number is the smallest positive integer
such that any -edge-coloring of contains a monochromatic subgraph
isomorphic to , colored with the th color for some . We
compute the exact values of the bipartite Ramsey numbers for
FK Comae Berenices, King of Spin: The COCOA-PUFS Project
COCOA-PUFS is an energy-diverse, time-domain study of the ultra-fast
spinning, heavily spotted, yellow giant FK Com (HD117555; G4 III). This single
star is thought to be a recent binary merger, and is exceptionally active by
measure of its intense ultraviolet and X-ray emissions, and proclivity to
flare. COCOA-PUFS was carried out with Hubble Space Telescope in the UV
(120-300 nm), using mainly its high-performance Cosmic Origins Spectrograph,
but also high-precision Space Telescope Imaging Spectrograph; Chandra X-ray
Observatory in the soft X-rays (0.5-10 keV), utilizing its High-Energy
Transmission Grating Spectrometer; together with supporting photometry and
spectropolarimetry in the visible from the ground. This is an introductory
report on the project.
FK Com displayed variability on a wide range of time scales, over all
wavelengths, during the week-long main campaign, including a large X-ray flare;
"super-rotational broadening" of the far-ultraviolet "hot-lines" (e.g., Si IV
139 nm (T~80,000 K) together with chromospheric Mg II 280 nm and C II 133 nm
(10,000-30,000 K); large Doppler swings suggestive of bright regions
alternately on advancing and retreating limbs of the star; and substantial
redshifts of the epoch-average emission profiles. These behaviors paint a
picture of a highly extended, dynamic, hot (10 MK) coronal magnetosphere around
the star, threaded by cooler structures perhaps analogous to solar prominences,
and replenished continually by surface activity and flares. Suppression of
angular momentum loss by the confining magnetosphere could temporarily postpone
the inevitable stellar spindown, thereby lengthening this highly volatile stage
of coronal evolution.Comment: to be published in ApJ
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