R. Graham, B. Rothschild, J. Spencer. Ramsey Theory. 2nd ed., Wiley, New-York, 1990. Home/Search Document Not in Database Summary Related Articles Check |
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Resource-bounded Continuity and Sequentiality for Type-two.. - Exte Nd Ed (Correct)
....demonstrating the existence of such a functional. The functional FR defined below is closely related to a Boolean function defined in [7] which is concerned with the power of Boolean decision trees for computing search functions. The definition of FR depends on a version of Ramsey s theorem (see [5]) FR is defined in terms a a certain partial colouring function defined on complete graphs (denoted K x ) Definition 5.3 For any function f and number x 0, define the partial colouring function f;x on K x as follows: suppose that the edges of K x are numbered 1; 2; Then for 1 ....
....bounded by jxj 4 , since there will be jxj values in the domain of the certificate (one for each edge of the monochromatic subgraph) and each value in the domain of the certificate is no greater than . Now suppose that FR (f; x) 1. We now appeal to a result of Ramsey theory (see [5]) which states that any (total) 2 colouring of K x has a monochromatic K k where k = log x nodes. Hence, if FR (f; x) 1, it follows that f;x is undefined for some i, 1 i . Then it must be the case that f(i) 2 Gamma 1, and so jf(i)j x and jij 2jxj. Thus there is a ....
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R. Graham, B. Rothschild, and J. Spencer. Ramsey Theory. John Wiley and Sons, Inc., New York, 2nd edition, 1990.
Provability with Finitely Many Variables - Hirsch, Hodkinson, Maddux (Correct)
....paper can be read as if it were a chapter in a (fairly terse and sophisticated) text on first order logic with equality. x2. A Ramsey theorem. Define ae : by ae(0) 1 and ae(k 1) 1 (k 1) Delta ae(k) for every k . This function gives an upper bound for a certain Ramsey number [7], 6, p 6] 8, Cor 3] 2, p 440 443] Its first five values are, respectively, 1, 2, 5, 16, and 65. For any set X , let [X ] be the set of 2 element subsets of X : X ] ffx; yg : x; y 2 X; x 6= yg: For 1 k , a k coloring of X is a partition of [X ] into k pieces (called ....
R. L. Graham, B. L. Rothschild, and J. H. Spencer, Ramsey theory, Wiley, New York, 1980.
Induced Subgraphs of Prescribed Size - Alon, Krivelevich, Sudakov (Correct)
....here are finite, undirected and simple. For a graph ; E, let #G denote the independence number of G and let wG denote the maximum number of vertices of a clique in G. Let qGmaxf#G;wGg denote the maximum number of vertices in a trivial induced subgraph of G. By Ramsey Theorem (see, e.g. [10]) qG##log n for every graph G with n vertices. Let uG denote the maximum integer u, such that for every integer y between 0 and u, G contains an induced subgraph with precisely y edges. Erdo s and McKay [5] see also [6] 7] and [4] p. 86) raised the following conjecture. Conjecture 1.1. For ....
R. Graham, B. Rothschild, and J. Spencer, Ramsey theory, 2nd edition, Wiley, New York, 1990.
A Glimpse at Veblen Hierarchies 37 7 A Glimpse at Veblen.. - What Have We (Correct)
....in Buchholz and Wainer [3] Since H 0 is not provably recursive in PA, Goodstein s theorem is a statement that is true but not provable in PA. Readers interested in combinatorial independence results are advised to consult the beautiful book on Ramsey theory, by Graham, Rothschild, and Spencer [19]. 13 Constructive Proofs of Higman s Lemma If one looks closely at the proof of Higman s lemma (lemma 3.2) one notices that the proof is not constructive for two reasons: 1) The proof proceeds by contradiction, and thus it is not intuitionistic. 2) The de nition of a minimal bad sequence ....
Graham, R.L., Rothschild, B.L., and Spencer, J.H. Ramsey Theory, John Wiley & Sons, Inc., 2nd edition, pp. 196 (1990).
Induced Graph Ramsey Theory - Schaefer, Shah (Correct)
....of vertices in G and H . The smallest order F (number of vertices) of a graph F for which F (G, H) is called r # (G, H) or r # (G) in the diagonal case G = H . If we omit the condition that subgraphs must be induced, we get the ordinary Ramsey numbers r(G, H) which are well investigated [Rad99, GRS90]. Erdos and Rodl conjectured r # (G) c G , where c is a constant [CG98] A recent paper by Kohayakawa, Promel, and Rodl established r # (G) 2 G (log G ) KPR98] While this result tells us something about the order of induced Ramsey graphs F for G, it does not allow us to construct ....
.... (v 1 , v # 1 ) and (v 2 , v # 2 ) if v 1 v 2 E or v 1 = v 2 and v # 1 v # 2 E # , i.e. the vertices of F are replaced with copies of G and the edges of F with complete bipartite graphs (or conversely) As references we use Diestel [Die97] for graph theory, and Graham, Rothschild, Spencer [GRS90] for Ramsey theory. 3 Trees versus Complete Graphs Theorem 3.1 Given a tree T and n 2 we can construct a graph F of order at most T such that F # (T , Kn ) Proof. Let T be a tree of order t. We will construct graphs Fn inductively such that Fn # (T , Kn ) For n = 2 we can let F 2 ....
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Ronald L. Graham, Bruce L. Rothschild, and Joel H. Spencer. Ramsey Theory. Wiley, 1990.
On an anti-Ramsey problem of Burr, Erdös, Graham and T.. - Sarközy, Selkow (2004) Self-citation (Graham) (Correct)
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R.L. Graham, B.L. Rothschild, J.H. Spencer, Ramsey Theory, 2nd ed., John Wiley and Sons, New York, 1990.
Finite Limits and Lower Bounds for Circuits Size - Jukna (1994) (Correct)
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R. Graham, B. Rothschild, J. Spencer. Ramsey Theory. 2nd ed., Wiley, New-York, 1990.
On Preservation under Homomorphisms and Unions of.. - Atserias, Dawar.. (2004) (Correct)
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R. L. Graham, B. L. Rothschild, and J. H. Spencer. Ramsey Theory. Wiley, 1980.
The Erdös-Szekeres theorem: upper bounds and related results - Toth, Valtr (2004) (Correct)
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R.L. Graham, B.L. Rothschild, and J.H. Spencer, Ramsey Theory, 2nd ed., John Wiley, New York, 1990.
Languages Defined With Modular Counting - Quantifiers Howard Straubing (Correct)
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R. Graham, B. Rothschild, J. Spencer, Ramsey Theory, John Wiley and Sons, New York, 1990.
Rainbow Ramsey Theory - Jungic, Nesetril, Radoicic (2004) (Correct)
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R. L. Graham, B. L. Rothschild, and J. H. Spencer. Ramsey Theory. Wiley, 1990.
Open Problems 17 - In Open Problems (Correct)
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R.L. Graham, B.L. Rothschild, and J.H. Spencer, Ramsey Theory (Wiley [1980])
Resource-bounded Continuity and Sequentiality for Type-two.. - Exte Nd Ed (Correct)
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R. Graham, B. Rothschild, and J. Spencer. Ramsey Theory. John Wiley and Sons, Inc., New York, 2nd edition, 1990.
Computational Methods for Ramsey Numbers - Haanpää (Correct)
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R. L. Graham, B. L. Rothschild, and J. H. Spencer. Ramsey Theory. John Wiley & Sons, 1980.
Satisfiability and computing van der Waerden numbers - Dransfield, Liu, al. (2004) (Correct)
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R.L. Graham, B.L. Rotschild, and J.H. Spencer. Ramsey Theory, Wiley, 1990.
Discrepancy of Cartesian Products of Arithmetic Progressions - Doerr, Srivastav, Wehr (2003) (Correct)
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R. L. Graham, B. L. Rothschild, and J. H. Spencer. Ramsey Theory. John Wiley & Sons Inc., New York, 1990.
A Ramsey property of planar graphs - Nesetril, al. (2004) (Correct)
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R.L. Graham, B. Rothschild, and J. Spencer, Ramsey theory, Wiley, New York (1990).
Discrepancy of Cartesian Products of Arithmetic Progressions - Doerr, Srivastav, Wehr (2004) (Correct)
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R. L. Graham, B. L. Rothschild, and J. H. Spencer. Ramsey Theory. John Wiley & Sons Inc., New York, 1990.
An Existential Fragment of Second Order Logic - Rosen (1997) (5 citations) (Correct)
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R. Graham, B. Rothschild, and J. Spencer. Ramsey Theory. John Wiley & Sons, 1980.
Satisfiability and computing van der Waerden numbers - Dransfield, Liu, al. (2004) (Correct)
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R.L. Graham, B.L. Rotschild, and J.H. Spencer. Ramsey Theory, Wiley, 1990.
Rainbow Arithmetic Progressions and Anti-Ramsey Results - Jungic, Licht, Mahdian.. (2002) (1 citation) (Correct)
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R.L. Graham, B.L. Rothschild, and J.H. Spencer. Ramsey Theory. John Wiley and Sons, 1990.
Satisfiability and computing van der Waerden numbers - Dransfield, Liu, al. (2004) (Correct)
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R.L. Graham, B.L. Rotschild, and J.H. Spencer. Ramsey Theory, Wiley, 1990.
Ramsey-Type Results for Geometric Graphs. II - Karolyi, Pach, Toth, Valtr (1998) (2 citations) (Correct)
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R.L. Graham, B.L. Rothschild, and J.H. Spencer, Ramsey Theory, 2nd ed., John Wiley, New York, 1990.
A Ramsey-type bound for rectangles - Toth (Correct)
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R. L. Graham, B. L. Rothschild, J. H. Spencer, Ramsey Theory, Wiley, New York (1980).
Note on the Erdös-Szekeres theorem - Tóth, Valtr (Correct)
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R.L. Graham, B.L. Rothschild, and J.H. Spencer, Ramsey Theory, 2nd ed., John Wiley, New York, 1990.
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