Results 11 to 20 of about 1,024 (103)
Generalized ramsey theory for graphs, x: double stars
Discrete Mathematics, 1979 AbstractThe double star S(n, m), where n ⩾ m ⩾ 0, is the graph consisting of the union of two stars K1,n and K1,m together with a line joining their centers. Its ramsey number r(S(n, m)) is the least number p such that there is a monochromatic copy of S(n, m) in any 2-coloring of the edges of Kp.
Grossman, Jerrold W. +2 more
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What can we hope to accomplish in generalized Ramsey theory?
Discrete Mathematics, 1987 Let F, G, and H denote graphs. We write \(F\to (G,H)\) to mean that, however the edges of F are colored red and blue, either the red subgraph of F contains a copy of G or the blue subgraph of F contains a copy of H. We write \(r(G,H)=t\) if \(K_ t\to (G,H)\) but \(K_{t-1}\nrightarrow (G,H)\); r(G,H) is called the Ramsey number of G and H. In this paper,
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Generalized Ramsey theory for graphs. III. Small off-diagonal numbers [PDF]
Pacific Journal of Mathematics, 1972 Chvátal, Václav, Harary, Frank
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Generalization of Ramsey Number for Cycle with Pendant Edges
MathematicsThis paper explores various Ramsey numbers associated with cycles with pendant edges, including the classical Ramsey number, the star-critical Ramsey number, the Gallai–Ramsey number, and the star-critical Gallai–Ramsey number.
Jagjeet Jakhar +5 more
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Rainbow generalizations of Ramsey theory - a dynamic survey
Theory and Applications of Graphs, 2014 In this work, we collect Ramsey-type results concerning rainbow edge colorings of graphs.
Fujita, Shinya +3 more
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Generalized Ramsey theory and decomposable properties of graphs
Discussiones Mathematicae Graph Theory, 1999 Summary: We translate Ramsey-type problems into the language of decomposable hereditary properties of graphs. We prove a distributive law for reducible and decomposable properties of graphs. Using it we establish some values of graph theoretical invariants of decomposable properties and show their correspondence to generalized Ramsey numbers.
Burr, Stefan A. +3 more
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Monochromatic Sums and Products of Polynomials
Discrete AnalysisMonochromatic sums and products of polynomials, Discrete Analysis 2024:5, 7 pp. An early result in Ramsey theory, Schur's theorem, states that if the positive integers are finitely coloured, then there will always be $x$ and $y$ such that $x,y$ and $x ...
Ryan Alweiss
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On a generalization of Ramsey theory
Discrete Mathematics, 1982 AbstractIn [2, 3], Chung and Liu introduce the following generalization of Ramsey Theory for graphs.
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Ramsey Theory Problems over the Integers: Avoiding Generalized Progressions [PDF]
, 2017 Two well studied Ramsey-theoretic problems consider subsets of the natural numbers which either contain no three elements in arithmetic progression, or in geometric progression. We study generalizations of this problem, by varying the kinds of progressions to be avoided and the metrics used to evaluate the density of the resulting subsets. One can view
Best, Andrew +6 more
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On the use of senders in generalized ramsey theory for graphs
Discrete Mathematics, 1985 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Burr, Stefan A +2 more
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