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An application of the regularity lemma in generalized Ramsey theory
Journal of Graph Theory, 2003AbstractGiven graphs G and H, an edge coloring of G is called an (H,q)‐coloring if the edges of every copy of H ⊂ G together receive at least q colors. Let r(G,H,q) denote the minimum number of colors in a (H,q)‐coloring of G. In 9 Erdős and Gyárfás studied r(Kn,Kp,q) if p and q are fixed and n tends to infinity.
Sárközy, Gábor N., Selkow, Stanley M.
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Recent results on generalized Ramsey theory for graphs
1972Virtually all of the known results on generalized Ramsey theory for graphs have been reported here, and the most general method of proof was brute force. There is certainly a need for more powerful and general methods, but it is not certain that these exist.
F. Harary
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Generalized ramsey theory VIII. The size ramsey number of small graphs
1983The ramsey number r(F) of a graph F with no isolates has been much studied. We now investigate its size Ramsey number ζ(F) defined as the minimum q such that there exists a graph G with q edges for which every 2-coloring of E(G) has a monochromatic F.
Frank Harary, Zevi Miller
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Ramsey theory for a generalized fan versus triangles
Utilitas Mathematica<p>In this paper, we consider Ramsey and Gallai-Ramsey numbers for a generalized fan <span class="math inline">\(F_{t,n}:=K_1+nK_t\)</span> versus triangles. Besides providing some general lower bounds, our main results include the evaluations of <span class="math inline">\(r(F_{3,2}, K_3)=13\)</span> and <span class ...
Mark Budden, Richard Prange
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Generalized ramsey theory XV: Achievement and avoidance games for bipartite graphs
1984Let two opponents, Oh and Ex, play the following game on the complete bipartite graph Kn,n. Oh colors one of the edges green and Ex colors a different edge red, and so on. The goal of each player is to be the first one to construct in his own color a predetermined bipartite graph M with no isolated points.
Martin Erickson, Frank Harary
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Ramsey Theory Is Needed for Solving Definability Problems of Generalized Quantifiers
European Summer School in Logic, Language and Information, 1999In recent years, generalized quantifiers (see [H3]) have received quite a lot of novel interest because of their applications to computer science and linguistics. Their definability theory has made considerable progress during the last decade, which will be the subject of the next section. The proofs of many of these results often use results of Ramsey
Kerkko Luosto
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Generalized Ramsey Numbers Involving Subdivision Graphs, And Related Problems in Graph Theory
1980Publisher Summary This chapter discusses generalized Ramsey numbers involving subdivision graphs and related problems in graph theory. It is assumed that if G1 and G2 are (simple) graphs, then the Ramsey number r(G1, G2) is the smallest integer n such that if one colors the complete graph Kn in two colors I and II, then either color I contains G1 as ...
S.A. Burr, P. Erdös
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Generalized Ramsey Theory for Graphs V. the Ramsey Number of a Digraph
Bulletin of the London Mathematical Society, 1974Harary, Frank, Hell, Pavol
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Rainbow Generalizations of Ramsey Theory: A Survey
Graphs and Combinatorics, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fujita, Shinya +2 more
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A generalization of Ramsey theory for linear forests
International Journal of Computer Mathematics, 2012Chung and Liu defined the d - chromatic Ramsey numbers as a generalization of Ramsey numbers by replacing the usual condition with a slightly weaker condition. Let 1 d c and let . Assume A 1, A 2,..., A t are all d -subsets of a set containing c distinct colours. Let G 1, G 2,..., G t be graphs.
A. Khamseh, G. R. Omidi
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