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Gábor Sági

Publications and source records attributed to Gábor Sági.

2 recordsLinked to original sources
arXiv2017

On Induced Subgraphs of Finite Graphs not Containing Large Empty and Complete Subgraphs

In their celebrated paper [Ramsey-Type Theorems, Discrete Appl. Math. 25 (1989) 37-52], Erdős and Hajnal asked the following: is it true, that for any finite graph H there exists a constant c(H) such that for any finite graph G, if G does not contain complete or empty induced subgraphs of size at least |V(G)|^c(H), then H can be isomorphically embedded into G ? The positive answer has become known as the Erdős-Hajnal conjecture. In Theorem 3.20 of the present paper we settle this conjecture in the affirmative. To do so, we are studying here the fine structure of ultraproducts of finite sets, so our investigations have a model theoretic character.

math.LO↗
arXiv2011

Clones above the unary clone

Let c be the cardinality of the continuum. We give a family of pairwise incomparable clones (on a countable base set) 2^c members, all with the same unary fragment, namely the set of all unary operations. We also give, for each n, a family of 2^c clones all with the same n-ary fragment, and all containing the set of all unary operations.

math.RA↗