The Chromatic Number of Two Families of Generalized Kneser Graphs Related to Finite Generalized Quadrangles and Finite Projective 3-Spaces

On the Chromatic Number of Generalized Stable Kneser Graphs

For each integer triple (n, k, s) such that k ≥ 2, s ≥ 2, and n ≥ ks, define a graph in the following manner. The vertex set consists of all k-subsets S of Zn such that any two elements in S are on circular distance at least s. Two vertices form an edge if and only if they are disjoint. For the special case s = 2, we get Schrijver’s stable Kneser graph. The general construction is due to Meunie...

Finite Generalized Quadrangles

Spreads and ovoids of finite generalized quadrangles

We survey recent results on spreads and ovoids of finite generalized quadrangles. Included in the survey are results on ovoids of PG(3, q); translation ovoids of Q(4, q); characterisations of generalized quadrangles using subquadrangles and ovoids of subquadrangles; and spreads of T2(Ω).

Automorphisms and characterizations of finite generalized quadrangles

Our paper surveys some new developments in the theory of automorphisms and characterizations of finite generalized quadrangles. It is the purpose to mention important new results which did not appear in the following standard works (or surveys) on the subject: Collineations of finite generalized quadrangles (S. E. Payne, 1983), Finite Generalized Quadrangles (S. E. Payne and J. A. Thas, 1984), ...

Moufang-like conditions for generalized quadrangles and classification of all finite quasi-transitive generalized quadrangles

We tell the history ofMoufang generalized quadrangles.We review someMoufang-like conditions, and classify finite quasi-transitive generalized quadrangles. These are generalized quadrangles so that for any two non-concurrent linesU,V of theGQ, and for someW ∈ {U,V }⊥, the group of generalized homologies with axes U and V acts transitively on the points ofW incident with neither U nor V. As a by-...