Some remarks on Ramsey matroids. (English) Zbl 0543.05021

Nešetřil, Jaroslav; Poljak, Svatopluk; Turzík, Daniel

Suppl. Rend. Circ. Mat. Palermo, II. Ser. 3, 185-189 (1984).

Results on Ramsey matroids together with some open problems are summarized. Using the method of matroid amalgamation, the following theorem is proved. Let M be a matroid and G be a subgroup of its automorphism group Aut M. Then there exists a matroid N such that (i) M is a restriction of N, (ii) Aut N is isomorphic to G, (iii) every automorphism of G extends uniquely to an automorphism of N.

MSC:

05B35	Combinatorial aspects of matroids and geometric lattices
20B25	Finite automorphism groups of algebraic, geometric, or combinatorial structures
05C55	Generalized Ramsey theory

Keywords:

Ramsey matroids; matroid amalgamation; automorphism group