An explicit construction of(3,t)-existentially closed graphs
نویسندگان
چکیده
منابع مشابه
A construction of 3-existentially closed graphs using quadrances
A graph is n-e.c. (n-existentially closed) if for every pair of subsets A, B of vertex set V of the graph such that A∩B = ∅ and |A|+ |B| = n, there is a vertex z not in A∪B joined to each vertex of A and no vertex of B. Few explicit families of n-e.c. are known for n > 2. In this short note, we give a new construction of 3-e.c. graphs using the notion of quadrance in the finite Euclidean space Zp.
متن کاملExistentially Closed BIBD Block-Intersection Graphs
A graph G with vertex set V is said to be n-existentially closed if, for every S ⊂ V with |S| = n and every T ⊆ S, there exists a vertex x ∈ V − S such that x is adjacent to each vertex of T but is adjacent to no vertex of S − T . Given a combinatorial design D with block set B, its block-intersection graph GD is the graph having vertex set B such that two vertices b1 and b2 are adjacent if and...
متن کاملSteiner Triple Systems and Existentially Closed Graphs
We investigate the conditions under which a Steiner triple system can have a 2or 3-existentially closed block intersection graph.
متن کاملAn Explicit Construction of Expander Graphs
2 The Construction Fix n = m2 for a natural m and let An =Zm Zm,Zm being the group of integers modulo m. An may be thought of a combinatorial torus. Consider the following 5 bijections on An: 1. σ0 : (x;y) 7! (x;y), 2. σ1 : (x;y) 7! (x;x+ y), 3. σ2 : (x;y) 7! (x;x+ y+1), 4. σ3 : (x;y) 7! (x+ y;y), and 5. σ4 : (x;y) 7! (x+ y+1;y), addition modulo m. Now define Gn = (Un;Vn; En) as follows: Un = V...
متن کاملExistentially closed CSA-groups
We study existentially closed CSA-groups. We prove that existentially closed CSA-groups without involutions are simple and divisible, and that their maximal abelian subgroups are conjugate. We also prove that every countable CSA-group without involutions embeds into a finitely generated one having the same maximal abelian subgroups, except maybe the infinite cyclic ones. We deduce from this tha...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2013
ISSN: 0166-218X
DOI: 10.1016/j.dam.2012.12.016