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Small order graph-tree Ramsey numbers

1988
*
Discrete Mathematics
*

With but a few exceptions, the

doi:10.1016/0012-365x(88)90200-2
fatcat:yyftggepqbf4bhwmosdjmgzdtq
*Ramsey**number*r(G, T) is determined for all connected*graphs*G with at most five vertices and all*trees*T. ... Complications arise in finding this*Ramsey**number*when H is of arbitrary*order*or has large maximal degree, even when H is a*tree*and G is of*small**order*. ... Thus for*graphs*of this paper, G of*small**order*and H an arbitrary*tree*, the chromatic*number*of G and the*order*of H are parameters which affect r(G, H). ...##
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Ramsey Theory on Infinite Structures and the Method of Strong Coding Trees
[article]

2020
*
arXiv
*
pre-print

*Ramsey*theory of copies of the Rado

*graph*. ... Using forcing as a tool for finite searches has allowed the development of

*Ramsey*theory on such

*trees*, leading to solutions for finite big

*Ramsey*degrees of Henson

*graphs*as well as infinite dimensional ... Suppose that K satisfies the

*Ramsey*property (or has finite

*small*

*Ramsey*degrees). Let K be the Fraïssé limit of K with some linear

*order*of its universe in

*order*-type ω. ...

##
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Generalized Ramsey numbers through adiabatic quantum optimization

2016
*
Quantum Information Processing
*

For generalized

doi:10.1007/s11128-016-1363-3
fatcat:hlwq5wydofctjnrf3rsaow7mzq
*Ramsey**numbers*r(G,H), the emergent*order*is characterized by*graphs*G and H. ... optimization; and (ii) determine the*Ramsey**numbers*r(T_m,T_n) for*trees*of*order*m,n = 6,7,8, most of which were previously unknown. ... We determined all generalized*Ramsey**numbers*for*trees*of*order*6-8, resulting in 1600*tree**Ramsey**numbers*, of which (to the best of our knowledge) 1479 are new. ...##
###
Some Ramsey–Turán type problems and related questions

2012
*
Discrete Mathematics
*

For which

doi:10.1016/j.disc.2011.09.015
fatcat:gjjizn7b6zaqzjeypu5plj5tom
*graphs*G does there exist a constant 0 < c < 1 such that when H is a*graph*of*order*the*Ramsey**number*r(G) with δ(H) > c|H|, then any 2-edge coloring of H contains a monochromatic copy of G? ... Another variant is to 2-edge color a replacement for the*graph*K r(G) by a balanced multipartite*graph*of approximately the same*order*with the same consequence, a monochromatic G. ...*Ramsey**number*for any*tree*on n vertices when l = 2k = 2n/3. ...##
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Some Known Results and an Open Problem of Tree - Wheel Graph Ramsey Numbers

2005
*
Limits Journal of Mathematics and Its Applications
*

*Ramsey*

*numbers*. In this paper we list some known results and an open problem on

*graph*

*Ramsey*

*numbers*. In the special cases, we list to determine

*graph*

*Ramsey*

*numbers*for

*trees*versus wheels. ... For more information, see nice survey

*small*

*Ramsey*

*numbers*in [21] . Some known results on

*tree*-wheel For combination of

*tree*and wheel, several results have been obtained for wheels. ... For given

*graphs*G and H, the

*graph*

*Ramsey*

*number*R(G, H) is the smallest positive integer N such that for every

*graph*F of

*order*N the following holds: either F contains G as a subgraph or the complement ...

##
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Ramsey theory of homogeneous structures: current trends and open problems
[article]

2021
*
arXiv
*
pre-print

Exciting recent developments include new methods involving logic, topological

arXiv:2110.00655v1
fatcat:yl4tfcwtrng5vlalcpbukys5xe
*Ramsey*spaces, and category theory. ... The paper concentrates on big*Ramsey*degrees, presenting their essential structure where known and outlining areas for further development. ... The "big" refers to the fact that we require an isomorphic subcopy of an infinite structure in which the*number*of colors is as*small*as possible (in contrast to the concept of*small**Ramsey*degree in finite ...##
###
Page 8417 of Mathematical Reviews Vol. , Issue 2000m
[page]

2000
*
Mathematical Reviews
*

A general method of

*ordering**trees*is derived as well, and as its applications we give optimal estimates of the*orderings*of two types of*trees*.” 2000m:05158 05C50 15A48 Xu, Changqing [Xu, Chang Qin] ( ... Summary: “We study the spectrum of the Laplacian for*trees*and present an approach to*ordering**trees*by the spectral radius of the Laplacian. ...##
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Bipartite Ramsey numbers involving stars, stripes and trees

English

2013
*
Electronic Journal of Graph Theory and Applications
*

English

The

doi:10.5614/ejgta.2013.1.2.2
fatcat:vtuybuzul5hq5jlo4kwx6ldlxe
*Ramsey**number*R(m, n) is the smallest integer p such that any blue-red colouring of the edges of the complete*graph*K p forces the appearance of a blue K m or a red K n . ... We investigate the appearance of simpler monochromatic*graphs*such as stripes, stars and*trees*under a 2-colouring of the edges of a bipartite*graph*. ... The minimum*order*of a complete*graph*that must achieve that is known as a*Ramsey**number*. ...##
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Generalizing p-goodness to ordered graphs
[article]

2020
*
arXiv
*
pre-print

It is known that the connected

arXiv:1412.3071v4
fatcat:stxxlnpnsbce7lur5busmj2uzi
*graphs*that are p-good for all p are the*trees*. In this paper, we ask which*ordered**trees*are*order*-p-good for all p. ...*Ordered**Ramsey**numbers*are fairly new. ... In particular, the collection of connected*graphs*that are p-good for all p is precisely the collection of*trees*.*Ordered**Ramsey**numbers*Definition 6. ...##
###
Page 2010 of Mathematical Reviews Vol. , Issue 90D
[page]

1990
*
Mathematical Reviews
*

H. (1-MEMP)

*Small**order**graph*-*tree**Ramsey**numbers*. Proceedings of the First Japan Conference on*Graph*Theory and Applications (Hakone, 1986). Discrete Math. 72 (1988), no. 1-3, 119-127. ... H. (1-MEMP) Some complete bipartite*graph*-*tree**Ramsey**numbers*.*Graph*theory in memory of G. A. Dirac (Sandbjerg, 1985), 79-89, Ann. Discrete Math., 41, North-Holland, Amsterdam-New York, 1989. ...##
###
Page 8623 of Mathematical Reviews Vol. , Issue 2001M
[page]

2001
*
Mathematical Reviews
*

In this paper a

*number*of interesting upper and lower bound formulae are established for the*graph*-theoretic*Ramsey**number*R(G}", G3), where the*graphs*G7" and GJ have*orders*m and n respectively, in terms ... , G2) for all 3</<~™m, where F consists of all edge-minimal*graphs*of*order*j and minimum degree i.” 2001m:05170 05C55 Haanpaa, Harri (FIN-HUT-TCS; Espoo) A lower bound for a*Ramsey**number*. ...##
###
Extremal Theory and Bipartite Graph-Tree Ramsey Numbers
[chapter]

1988
*
Annals of Discrete Mathematics
*

Also, applications of this to the determination of

doi:10.1016/s0167-5060(08)70775-1
fatcat:mggki2g7evblned5htfbq346j4
*Ramsey**number*for arbitrary*graphs*and*trees*will be discussed . ... It will be show that if B is a bipartite*graph*with parts of*order*k and i (k--1), then there exists a positive constant c, such that for any*tree*T of*order*n and for any j (0--j _-(k -1)), the*Ramsey*... Erdős etal t a sparse*graph*[3] [4] [5] 8] . It would be of interest to know which sparse*graphs*could replace the*trees*of Theorem 1 and Theorem 5 without altering the results . ...##
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On the Ramsey Numbers of Trees with Small Diameter

2011
*
Graphs and Combinatorics
*

We estimate the

doi:10.1007/s00373-011-1098-y
fatcat:kzdu3f6hu5efpk2sspimjydy64
*Ramsey**number*r(T) = r(T,T) for various*trees*T, obtaining a precise value for r(T) for a large*number*of*trees*of diameter 3. ... Furthermore we prove that all*trees*of diameter 3 are*Ramsey*unsaturated as defined by Balister, Lehel, and Schelp in their article "*Ramsey*unsaturated and saturated*graphs*." ... We note that*Ramsey**numbers*of*trees*versus*trees*have not been very well investigated. In [2] Burr and Roberts establish the*Ramsey**number*of any*number*of star versus one another. ...##
###
Page 3207 of Mathematical Reviews Vol. , Issue 2003e
[page]

2003
*
Mathematical Reviews
*

Some results in

*Ramsey*theory can be stated in terms of*ordered**Ramsey**numbers*. The authors find the values of various*ordered**Ramsey**numbers*, e.g. ...*Ordered**Ramsey**numbers*. (English summary) Discrete Math. 247 (2002), no. 1-3, 79-92. Let D,, D> D, be simple directed*graphs*with no directed cy- cles. ...##
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Restricted Size Ramsey Number for Matching versus Tree and Triangle Unicyclic Graphs of Order Six

2022
*
International Journal of Computing Science and Applied Mathematics
*

In this paper we give the restricted size

doi:10.12962/j24775401.v8i1.10817
fatcat:5iqmn3zhavbvzl72ljifp5wvoa
*Ramsey**number*for a matching of two edges versus*tree*and triangle unicyclic*graphs*of*order*six. ... The restricted size*Ramsey**number*r * (G, H) is the smallest positive integer r * such that there is a*graph*F , of*order*r(G, H) and with the size r * , satisfying F arrows (G, H). ... This*Ramsey**number*gives the*order*of a*graph*F that satisfies F → (2K 2 , H), where H is any*tree**graphs*or triangle unicyclic*graphs*of*order*six. ...
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