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Local Ramsey numbers for some graphs

2003
*
Discrete Mathematics
*

We study the relation between the 2-

doi:10.1016/s0012-365x(02)00800-2
fatcat:dznyczgd2fht5poc5aiufxatfu
*local**Ramsey**number*R 2-loc (G) and the*Ramsey**number*R(G), where the complement of G is a disjoint union of*some*complete*graphs*or G is a disjoint union of*some*stars ... In this paper we study the relation between the 2-*local**Ramsey**number*R 2-loc (G) and the*Ramsey**number*R(G), where the complement of G is a disjoint union of*some*complete*graphs*or G is a disjoint union ... The k-*local**Ramsey**number*R k-loc (G) of a*graph*G is deÿned as the smallest integer n such that K n contains a monochromatic subgraph G*for*every*local*k-colouring of K n . ...##
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Relations between 2-local and 2-mean Ramsey numbers for graphs

2007
*
Discrete Mathematics
*

We study the relation between the 2-

doi:10.1016/j.disc.2005.11.036
fatcat:wuk5qyxadrhyrdyg67lz4hlpqy
*local**Ramsey**number*R 2-loc (G) and the 2-mean*Ramsey**number*R 2-mean (G)*for**graphs*. ... We give the exact value of the 2-mean*Ramsey**number**for**some*infinite families of*graphs*. ... Acknowledgements I would like to thank the anonymous referees*for*their comments that improved the presentation of this paper. ...##
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Local k-colorings of graphs and hypergraphs

1987
*
Journal of combinatorial theory. Series B (Print)
*

The size

doi:10.1016/0095-8956(87)90017-7
fatcat:nep3mrrrybehdjmxahrkxdr5vm
*Ramsey**number**for**local*kcolorings, ik,(G), can be defined analogously as mini IE(H)I : HE L@&(G) >. We may ask about the relation of these*numbers*. ... The size*Ramsey**number*F'(G) of a*graph*G was introduced in [8] . Using the notion of minimal*Ramsey**graphs*(see Section 5 ); ?(G) = min{ IE(H)J: HE&(G)}. ...*RAMSEY**NUMBERS*AND SIZE*RAMSEY**NUMBERS*We denote by rk(G) the*Ramsey**number*of a*graph*G, i.e., the minimum III*for*which K,n contains a monochromatic copy of G in every k-coloring of the edges of K,. ...##
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Page 1493 of Mathematical Reviews Vol. , Issue 2001C
[page]

2001
*
Mathematical Reviews
*

No

*graph*G is known*for*which*local*and mean k-*Ramsey**numbers*are different. ... The*local*k-*Ramsey*{mean k-*Ramsey*]*number*of a*graph*G is the smallest order of a complete*graph**for*which every*local*[mean] k-coloring ensures a monochromatic copy of G. ...##
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Large cliques and independent sets all over the place
[article]

2020
*
arXiv
*
pre-print

Over all n-vertex

arXiv:2004.04718v2
fatcat:wqbdtvpaendmpnmyfzoo6ryzku
*graphs*G what is the smallest possible value of m*for*which any m vertices of G contain both a clique and an independent set of size log n? ... Our (probabilistic) construction gives rise to new examples of*Ramsey**graphs*, which while having no very large homogenous subsets contain both cliques and independent sets of size log n in any small subset ... We would like to thank David Conlon*for*useful conversations and remarks and anonymous referees*for*their comments. ...##
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Page 5781 of Mathematical Reviews Vol. , Issue 95j
[page]

1995
*
Mathematical Reviews
*

Summary: “In this note we obtain

*some*lower bounds*for*the*Ramsey**numbers*r;(/;r), where r;(/;r) is the least positive integer n such that*for*every coloring of the k-element subsets of an n- element set ... Radziszowski (1-RIT-C; Rochester, NY) 95j:05137 05C55 Huang, Guo Tai*Some*generalized*Ramsey**numbers*. (Chinese summary) J. Math. Res. Exposition 14 (1994), no. 2, 169-174. ...##
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On the Ramsey Numbers for Bipartite Multigraphs
[article]

2003
*
arXiv
*
pre-print

Note that the

arXiv:cs/0305006v1
fatcat:olkho6wkwrcy5p6a6l2n32ee6q
*number*of colors found in a*graph*under m-*local*coloring may exceed m. ... Unlike the conventional m-coloring scheme in*Ramsey*theory which imposes a constraint (i.e., m) on the total*number*of colors allowed in a*graph*, we introduce a relaxed version called m-*local*coloring ... Acknowledgments We thank Gerard Jennhwa Chang*for*very helpful comments on a preliminary version of this paper. ...##
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Generalized local colorings of graphs

1992
*
Journal of combinatorial theory. Series B (Print)
*

We prove the

doi:10.1016/0095-8956(92)90049-4
fatcat:scavypuyd5dppafxf6hxjpwiyy
*Ramsey*property*for*such colorings, establish conditions*for*the density property and the bipartite version of the*Ramsey*theorem to hold, and prove the induced variant of the*Ramsey*theorem ... A*local*(H, k)-coloring of a*graph*G is a coloring of the edges of G such that edges of no subgraph of G isomorphic to a subgraph of H are colored with more than k colors. ... In addition,*for*many*graphs*G the usual*Ramsey**number*rk(G) and the*local**Ramsey**number*r:,,(G) are equal or differ by 1. ...##
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Page 2472 of Mathematical Reviews Vol. , Issue 89E
[page]

1989
*
Mathematical Reviews
*

The

*local**Ramsey**number*R = LR(H;,m) is defined as the minimal*number*R > k such that*for*every Gr, Gr is not*local**for*H, or clGr > m (clG denotes the size of the maximum complete subgraph of G). ...*For*natural*numbers*k,n such that k <n, let G,, H, be*graphs*with n and k vertices, respectively; G, is said to be*local**for*H, if*for*each set S of k vertices of G, the corresponding subgraph Gs is isomorphic ...##
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Local and Mean Ramsey Numbers for Trees

2000
*
Journal of combinatorial theory. Series B (Print)
*

It is expected that the k-

doi:10.1006/jctb.2000.1950
fatcat:7rjdq6u42fgd3f5rznkgogjl3q
*local*and k-mean*Ramsey**numbers*are identical*for*most*graphs*. In fact, it would be interesting to determine whether this pair of*numbers*can ever differ*for**some**graph*G. ... K It is likely that R(T, k loc)=R(T, k mean)*for*all trees T and*for*all k. In fact, we believe that k-*local*and k-mean*Ramsey**numbers*are the same*for*sparse*graphs*of large order. ...##
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New bounds for Ramsey numbers R(K_k-e,K_l-e)
[article]

2021
*
arXiv
*
pre-print

Let R(H_1,H_2) denote the

arXiv:2107.04460v1
fatcat:k54a7zz2xnaqbnpszuauwuo4iq
*Ramsey**number**for*the*graphs*H_1, H_2, and let J_k be K_k-e. ... We present algorithms which enumerate all circulant and block-circulant*Ramsey**graphs**for*different types of*graphs*, thereby obtaining several new lower bounds on*Ramsey**numbers*including: 49 ≤ R(K_3,J ... Acknowledgements We would like to thank Gunnar Brinkmann and Stanis law Radziszowski*for*useful suggestions. ...##
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Page 4752 of Mathematical Reviews Vol. , Issue 87i
[page]

1987
*
Mathematical Reviews
*

The author announces

*some*new sufficient conditions*for*Hamiltonian cycles in terms of degrees, independence*number*, and toughness. {*For*the entire collection see MR 87g:00016.} ... Sheehan and the reviewer [“The*Ramsey**number*of Ks —e”, J.*Graph*Theory, to appear].} {*For*the entire collection see MR 86g:05026.} Heiko Harborth (Braunschweig) Caro, Y. (IL-TLAV); Krasikov, I. ...##
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New Lower Bounds for 28 Classical Ramsey Numbers
[article]

2015
*
arXiv
*
pre-print

We establish new lower bounds

arXiv:1504.02403v3
fatcat:pcso7jbfqvhv5lgjir4zuk7cgy
*for*28 classical two and three color*Ramsey**numbers*, and describe the heuristic search procedures we used. ...*Some*of the other new constructions in the paper are derived from two well-known colorings: the Paley coloring of K_101 and the cubic coloring of K_127. ... We noticed that*some*of the bounds*for**Ramsey**numbers*of the form R(3, 3, k) were close to the corresponding bounds*for**numbers*of the form R(5, k). ...##
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Page 1392 of Mathematical Reviews Vol. , Issue 90C
[page]

1990
*
Mathematical Reviews
*

Parthasarathy (6-IITM)
90c:05152 05C55
Thomason, Andrew (4-CAMB)
An upper bound

*for**some**Ramsey**numbers*. J.*Graph*Theory 12 (1988), no. 4, 509-517. ... Lower bounds*for*the*Ramsey**number*r(k,k) are dealt with in*some*detail, including the initial result of Erdés that r(k,k) > 2*/2*for*k > 3, and the series of minor improvements that followed. ...##
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Page 2925 of Mathematical Reviews Vol. , Issue 80H
[page]

1980
*
Mathematical Reviews
*

As a way of measuring minimality

*for*mem- bers of C, we define the size*Ramsey**number*by /(G,,G,)= min|E(G)|*for*G EC. ... This paper concerns the*Ramsey**numbers*(B,,,C,)*for*books versus cycles, and relates certain of these*numbers*to finite projective planes, to Moore*graphs*, and to other interesting structures. ...
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