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Graph Ramsey theory and the polynomial hierarchy (Extended Abstract)
 ANNUAL ACM SYMPOSIUM ON THEORY OF COMPUTING (ATLANTA, GA, 1999), ACM
, 1999
"... In the Ramsey theory of graphs F + (G, H) means that for every way of coloring the edges of F red and blue F will contain either a red G or a blue H. The problem ARROWING of deciding whether F + (G, H) lies in II; = coNPNP and it was shown to be coNP hard by Burr [5]. We prove that ARROWING is actu ..."
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Cited by 26 (5 self)
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In the Ramsey theory of graphs F + (G, H) means that for every way of coloring the edges of F red and blue F will contain either a red G or a blue H. The problem ARROWING of deciding whether F + (G, H) lies in II; = coNPNP and it was shown to be coNP hard by Burr [5]. We prove that ARROWING is actually II;complete, simultaneously settling a conjecture of Burr and providing a natural example of a problem complete for a higher level of the polynomial hierarchy. We also show that STRONG ARROWING, the version for induced subgraphs, is rI;complete.
Induced Ramseytype theorems
, 2008
"... We present a unified approach to proving Ramseytype theorems for graphs with a forbidden induced subgraph which can be used to extend and improve the earlier results of Rödl, Erdős–Hajnal, Prömel–Rödl, Nikiforov, Chung–Graham, and Łuczak–Rödl. The proofs are based on a simple lemma (generalizing ..."
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Cited by 13 (8 self)
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We present a unified approach to proving Ramseytype theorems for graphs with a forbidden induced subgraph which can be used to extend and improve the earlier results of Rödl, Erdős–Hajnal, Prömel–Rödl, Nikiforov, Chung–Graham, and Łuczak–Rödl. The proofs are based on a simple lemma (generalizing one by Graham, Rödl, and Ruciński) that can be used as a replacement for Szemerédi’s regularity lemma, thereby giving much better bounds. The same approach can be also used to show that pseudorandom graphs have strong induced Ramsey properties. This leads to explicit constructions for upper bounds on various induced Ramsey numbers.
Ramsey Theory Applications
, 2004
"... There are many interesting applications of Ramsey theory, these include results in number theory, algebra, geometry, topology, set theory, logic, ergodic theory, information theory and theoretical computer science. Relations of Ramseytype theorems to various fields in mathematics are well documente ..."
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There are many interesting applications of Ramsey theory, these include results in number theory, algebra, geometry, topology, set theory, logic, ergodic theory, information theory and theoretical computer science. Relations of Ramseytype theorems to various fields in mathematics are well documented in published books and monographs. The main objective of this survey is to list applications mostly in theoretical computer science of the last two decades not contained in these.