The problem of computing the chromatic number of Kneser hypergraphs has been extensively studied over the last 40 years and the fractional version of the chromatic number of Kneser hypergraphs is only solved for particular cases. The (p, q)-extremal problem consists in finding the maximum number of edges on a k-uniform hypergraph H with n vertices such that among any p edges some q of them have...

We determine the independence number of the Kneser graph on line-plane flags in the projective space PG(4, q).

The achromatic number α of a graph is the largest number of colors that can be assigned to its vertices such that adjacent vertices have different color and every pair of different colors appears on the end vertices of some edge. We estimate the achromatic number of Kneser graphs K(n, k) and determine α(K(n, k)) for some values of n and k. Furthermore, we study the achromatic number of some geo...

In this short note, we show that for any ϵ>0 and k<n0.5−ϵ the choice number of Kneser Graph KGn,k is Θ(nlog⁡n).

We show that there are k simple graphs whose Kronecker covers isomorphic to the bipartite Kneser graph H ( n , ) and determine automorphism groups of these graphs. Using neighborhood complexes graphs, we also chromatic numbers coincide with ? K = ? 2 + .

Call a set of 2n + k elements Kneser-colored when its n-subsets are put into classes such that disjoint n-subsets are in different classes. Kneser showed that k + 2 classes are sufficient to Kneser-color the n-subsets of a 2n + k element set. There are several proofs that this same number is necessary which rely on fixed-point theorems related to the Lusternik-SchnirelmannBorsuk (LSB) theorem. ...

A fall k-coloring of a graph G is a proper k-coloring of G such that each vertex of G sees all k colors on its closed neighborhood. In this note, we characterize all fall colorings of Kneser graphs of type KG(n, 2) for n ≥ 2 and study some fall colorings of KG(n,m) in some special cases and introduce some bounds for fall colorings of Kneser graphs.

Let G be an undirected graph, A be an (additive) abelian group and A∗ = A−{0}. A graph G is A-connected if G has an orientation D(G) such that for every function b : V (G) → A satisfying ∑v∈V (G) b(v) = 0, there is a function f : E(G) → A∗ such that ∑e∈E+(v) f(e) − ∑ e∈E−(v) f(e) = b(v). For an abelian group A, let 〈A〉 be the family of graphs that are A-connected. The group connectivity number ...

Let Γ be a distance-regular graph with diameter d and Kneser graph K = Γd, the distance-d graph of Γ. We say that Γ is partially antipodal when K has fewer distinct eigenvalues than Γ. In particular, this is the case of antipodal distance-regular graphs (K with only two distinct eigenvalues), and the so-called half-antipodal distance-regular graphs (K with only one negative eigenvalue). We prov...