k --Universal Finite Graphs

Details k --Universal Finite Graphs k --Universal Finite Graphs

1996-04-15

arxiv.org/abs/math/9604244v1

DIMACS Ser. Discrete Math. Theoret. Comput. Sci., 33 (1997), 65-77

Mathematics

Logic

Scientific paper

This paper investigates the class of k-universal finite graphs, a local analog of the class of universal graphs, which arises naturally in the study of finite variable logics. The main results of the paper, which are due to Shelah, establish that the class of k-universal graphs is not definable by an infinite disjunction of first-order existential sentences with a finite number of variables and that there exist k-universal graphs with no k-extendible induced subgraphs.

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