Page 1

Displaying 1 – 3 of 3

Showing per page

The centre of a Steiner loop and the maxi-Pasch problem

Andrew R. Kozlik (2020)

Commentationes Mathematicae Universitatis Carolinae

A binary operation “ · ” which satisfies the identities x · e = x , x · x = e , ( x · y ) · x = y and x · y = y · x is called a Steiner loop. This paper revisits the proof of the necessary and sufficient conditions for the existence of a Steiner loop of order n with centre of order m and discusses the connection of this problem to the question of the maximum number of Pasch configurations which can occur in a Steiner triple system (STS) of a given order. An STS which attains this maximum for a given order is said to be maxi-Pasch. We show that...

The size of minimum 3-trees: cases 0 and 1 mod 12

Jorge L. Arocha, Joaquín Tey (2003)

Discussiones Mathematicae Graph Theory

A 3-uniform hypergraph is called a minimum 3-tree, if for any 3-coloring of its vertex set there is a heterochromatic triple and the hypergraph has the minimum possible number of triples. There is a conjecture that the number of triples in such 3-tree is ⎡(n(n-2))/3⎤ for any number of vertices n. Here we give a proof of this conjecture for any n ≡ 0,1 mod 12.

Currently displaying 1 – 3 of 3

Page 1