Results 31 to 40 of about 21,615 (266)

On Finite Ramsey Numbers

European Journal of Combinatorics, 1982
In the first section of this paper it is shown that the bipartite Ramsey number br(m, n) satisfies br(m, n)⩽2m(n−1)+1. (Beineke and Schwenk [1] conjectured br(m, n) = 2m(n−1) + 1 but Irving [17] showed that equality does not always hold.) The second section gives a conjecture for the Ramsey numbers of the complete graphs, and lastly the numbers of ...
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Ramsey and Gallai-Ramsey numbers for forests

Discussiones Mathematicae Graph Theory
Summary: Given two non-empty graphs \(G,H\) and a positive integer \(k\), the Gallai-Ramsey number \(\operatorname{gr}_k(G:H)\) is defined as the minimum integer \(N\) such that for all \(n\geq N\), every \(k\)-edge-coloring of \(K_n\) contains either a rainbow copy of \(G\) or a monochromatic copy of \(H\).
Yujia Gao, Meng Ji, Yaping Mao, Meiqin Wei   +3 more
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RAMSEY NUMBERS FOR TREES [PDF]

Bulletin of the Australian Mathematical Society, 2012
AbstractForn≥5, letT′ndenote the unique tree onnvertices with Δ(T′n)=n−2, and letT*n=(V,E) be the tree onnvertices withV={v0,v1,…,vn−1} andE={v0v1,…,v0vn−3,vn−3vn−2,vn−2vn−1}. In this paper, we evaluate the Ramsey numbersr(Gm,T′n) andr(Gm,T*n) , whereGmis a connected graph of orderm.
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Critical Graphs for R(Pn, Pm) and the Star-Critical Ramsey Number for Paths

Discussiones Mathematicae Graph Theory, 2015
The graph Ramsey number R(G,H) is the smallest integer r such that every 2-coloring of the edges of Kr contains either a red copy of G or a blue copy of H.
Hook Jonelle
doaj   +1 more source

On the restricted size Ramsey number for P3 versus dense connected graphs

Electronic Journal of Graph Theory and Applications, 2020
Let F, G and H be simple graphs. A graph F is said a (G,H)-arrowing graph if in any red-blue coloring of edges of F we can find a red G or a blue H. The size Ramsey number of G and H, ŕ(G,H), is the minimum size of F.
Denny Riama Silaban, Edy Tri Baskoro, Saladin Uttunggadewa   +2 more
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Ordered Ramsey numbers

Discrete Mathematics, 2002
Let \(TT_n\) denote the transitive tournament on \(n\) vertices and let \(D_1,D_2,\dots, D_k\) be acyclic digraphs. The ordered Ramsey number \(\rho(D_1,D_2,\dots, D_k)\) is the smallest integer \(n\) so that any \(k\)-coloring of the edges of \(TT_n\) admits, for some index \(i\), a copy of \(D_i\) with all of its edges colored with the \(i\)th color.
Sheshayya A. Choudum, B. Ponnusamy
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The Lupus Damage Index Revision Program: Results From the Item Generation and Reduction Phases

Arthritis Care &Research, EarlyView.
Objective A data‐driven and expert/patient consensus‐based project to develop a revised Systemic Lupus International Collaborating Clinics (SLICC)/American College of Rheumatology (ACR) Damage Index (SDI) is under way supported by SLICC, ACR, and the Lupus Foundation of America. Our objective is to report the item generation and reduction phase results
Burak Kundakci, Megan R. W. Barber, Ann E. Clarke, Sindhu R. Johnson, Anselm Mak, Hermine I. Brunner, Murat Inanc, Rosalind Ramsey‐Goldman, Guillermo Ruiz‐Irastorza, Ellen M. Ginzler, John G. Hanly, Alexandra Legge, Cynthia Aranow, Laurent Arnaud, Nathalie Costedoat‐Chalumeau, Dafna D. Gladman, Søren Jacobsen, Michelle Petri, Clovis A. Silva, Évelyne Vinet, Alexandre E. Voskuyl, SDI Revision Literature Review Groups, SDI Revision Delphi Panel, SDI Revision Item Reduction Committee, SDI Revision Clinical Domain Groups, Ian N. Bruce   +25 more
wiley   +1 more source

Diagonal Ramsey numbers in multipartite graphs related to stars

Electronic Journal of Graph Theory and Applications, 2022
: Let the star on n vertices, namely K1, n − 1 be denoted by Sn. If every two coloring of the edges of a complete balanced multipartite graph Kj × s there is a copy of Sn in the first color or a copy of Sm in the second color, then we will say Kj × s ...
Chula Janak Jayawardene
doaj   +1 more source

Metagenomic Association Uncovers Host Genotype‐Structured Rhizobacterial Networks and Novel Taxa That Enhance Soybean Salt Tolerance

Advanced Science, EarlyView.
An STI‐guided metagenomic association framework links soybean salt‐tolerance phenotypes with rhizosphere microbiome composition and network organization in natural saline soils. The approach identifies candidate beneficial taxa, including Thalassospira xiamenensis, and provides an efficient strategy for mining stress‐protective microbes from native ...
Yu Luo, Feng‐Li Kang, Qi‐Min Li, Wei‐Cai Yang   +3 more
wiley   +1 more source

Ramsey Numbers for Matroids

European Journal of Combinatorics, 1997
For positive integers \(s\) and \(t\), the matroid Ramsey number \(n(s,t)\) is the least positive integer \(n\) such that every connected matroid with at least \(n\) elements has either a circuit with at least \(s\) elements or a cocircuit with at least \(t\) elements.
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