A graph H is a minor of a graph G if a graph isomorphic to H can be obtained from a subgraph of G by contracting edges. An H-minor is a minor isomorphic to H. The Hadwiger number of G, denoted by h(G), is the maximum integer t such that G contains a Kt-minor, where Kt is the complete graph with t vertices. Hadwiger [8] conjectured that every graph that is not (t−1)-colourable contains a Kt-mino...

Complete colorings have the property that any two color classes has at least an edge between them. Parameters such as Grundy, achromatic and pseudoachromatic numbers comes from complete colorings, with some additional requirement. In this paper, we estimate these in Kneser graph $K(n,k)$ for values of $n$ $k$. We give exact value number $K(n,2)$.

The Wiener number of a graph G is defined as 1 2 ∑ d(u, v), where u, v ∈ V (G), and d is the distance function on G. The Wiener number has important applications in chemistry. We determine the Wiener number of an important family of graphs, namely, the Kneser graphs.

We determine the number of maximal intersecting families on a 9-set and find 423295099074735261880. We determine the number of independent sets of the Kneser graph K(9, 4) and find 366996244568643864340. Finally, we determine the number of intersecting families on an 8-set and find 14704022144627161780744368338695925293142507520.

Let k, d, λ > 1 be integers with d > λ. Let m(k, d, λ) be the maximum positive integer n such that every set of n points (not necessarily in general position) in R has the property that the convex hulls of all k-sets have a common transversal (d − λ)-plane. It turns out that m(k, d, λ) is strongly connected with other interesting problems, for instance, the chromatic number of Kneser hypergraph...

A graph G is said to be hom-idempotent if there is a homomorphism from G2 to G, and weakly hom-idempotent if for some n ≥ 1 there is a homomorphism from Gn+1 to Gn . We characterize both classes of graphs in terms of a special class of Cayley graphs called normal Cayley graphs. This allows us to construct, for any integer n, a Cayley graph G such that Gn+1 → Gn 6→ Gn−1, answering a question of ...

We prove that for a large family of product graphs, and for Kneser graphs K(n, αn) with fixed α < 1/2, the following holds. Any set of vertices that spans a small proportion of the edges in the graph can be made independent by removing a small proportion of the vertices of the graph. This allows us to strengthen the results of [DFR08] and [DF09], and show that any independent set in these graph...

We investigate some coloring properties of Kneser graphs. A star-free coloring is a proper coloring c : V (G) → N such that no path with three vertices may be colored with just two consecutive numbers. The minimum positive integer t for which there exists a star-free coloring c : V (G) → {1, 2, . . . , t} is called the starfree chromatic number of G and denoted by χs(G). In view of Tucker-Ky Fa...