Results 71 to 80 of about 21,406 (168)
The Ramsey numbers of fans versus a complete graph of order five
Electronic Journal of Graph Theory and Applications, 2014 For two given graphs $F$ and $H$, the Ramsey number $R(F,H)$ is the smallest integer $N$ such that for any graph $G$ of order $N$, either $G$ contains $F$ or the complement of $G$ contains $H$.
Yanbo Zhang, Yaojun Chen
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The Electronic Journal of Combinatorics, 2011 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.
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Discrete Mathematics, 1997 Fractional Ramsey numbers \(r_f(x,y)\) are defined as the smallest integer \(n\) such that for any red/blue coloring of the edges of the complete graph \(K_n\) either the red subgraph has the fractional clique number \(x\) or the blue subgraph has the fractional clique number \(y\).
Michael S. Jacobson +2 more
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Around a conjecture of Erdos in graph Ramsey theory
پژوهشهای ریاضی, 2021 For given graphs G1 and G2 the Ramsey number R(G1;G2), is the smallest positive integer n such that each blue-red edge coloring of the complete graph Kn contains a blue copy of G1 or a red copy of G2. In 1983, Erd}os conjectured that there is an absolute
Leila Maherani, Gholamreza Omidi
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Gallai-Ramsey number for rainbow S3 [PDF]
Discrete Mathematics Letters, 2022 Reji Thankachan +2 more
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Weakened Gallai-Ramsey numbers [PDF]
Surveys in Mathematics and its Applications, 2018 In the Ramsey theory of graphs, one seeks to determine the value of the Ramsey number rt(n), defined to be the least natural number p such that every coloring of the edges of Kp using t colors results in a monochromatic copy of Kn in some color.
Gabrielle Beam, Mark Budden
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Discrete Mathematics, 1978 AbstractA graph G is totally connected if both G and Ḡ (its complement) are connected. The connected Ramsey number rc(F, H) is the smallest integer k ⩾ 4 so that if G is a totally connected graph of order k then either F ⊂ G or H ⊂ Ḡ. We show that if neither of F nor H contains a bridge, then rc = r(F, H), the usual generalized Ramsey number of F and H.
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, 2005 Sequences Bn(p,q) of connected parts of Euclidean and hyperbolic (p,q)-mosaic graphs are considered. The smallest n such that any 2-coloring of the edges of Bn( p,q) contains a given monochromatic graph G is introduced as gameboard Ramsey number rp,q(G). For p ≥ 4 it is proved that these Ramsey numbers exist for finitely many graphs only.
Bode, Jens-Peter, Harborth, Heiko
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Magnetic field sensing based on phase Ramsey interferometry with Bose condensed 87Rb atomic gases
Shenzhen Daxue xuebao. Ligong banMagnetic field sensing utilizing Bose-condensed atomic gases can achieve both high sensitivity and spatial resolution. Employing two-photon transitions from F=1, mF=1→F=2, mF=-1 (F is the quantum number of total atomic angular momentum, mF is the ...
WU Jiatao +8 more
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The m-bipartite Ramsey number of the K2,2 versus K6,6 [PDF]
Contributions to Mathematics, 2022 Yaser Rowshan
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