Graphs with the Erdös-Ko-Rado property

Erdös-Ko-Rado theorems for chordal and bipartite graphs

One of the more recent generalizations of the Erdös-Ko-Rado theorem, formulated by Holroyd, Spencer and Talbot [10], de nes the Erdös-Ko-Rado property for graphs in the following manner: for a graph G, vertex v ∈ G and some integer r ≥ 1, denote the family of independent r-sets of V (G) by J (r)(G) and the subfamily {A ∈ J (r)(G) : v ∈ A} by J (r) v (G), called a star. Then, G is said to be r-E...

A generalization of the Erdős-Ko-Rado Theorem

In this note, we investigate some properties of local Kneser graphs defined in [8]. In this regard, as a generalization of the Erdös-Ko-Rado theorem, we characterize the maximum independent sets of local Kneser graphs. Next, we present an upper bound for their chromatic number.

Compression and Erdös-Ko-Rado graphs

For a graph G and integer r ≥ 1 we denote the collection of independent r-sets of G by I (r)(G). If v ∈ V (G) then I (r) v (G) is the collection of all independent r-sets containing v. A graph G, is said to be r-EKR, for r ≥ 1, iff no intersecting family A ⊆ I (r)(G) is larger than maxv∈V (G) |I v (G)|. There are various graphs which are known to have his property: the empty graph of order n ≥ ...

Towards a Katona type proof for the 2-intersecting Erdös-Ko-Rado theorem

Erdös-Ko-Rado and Hilton-Milner Type Theorems for Intersecting Chains in Posets

We prove Erdős-Ko-Rado and Hilton-Milner type theorems for t-intersecting k-chains in posets using the kernel method. These results are common generalizations of the original EKR and HM theorems, and our earlier results for intersecting k-chains in the Boolean algebra. For intersecting k-chains in the c-truncated Boolean algebra we also prove an exact EKR theorem (for all n) using the shift met...

Erdös-Ko-Rado-Type Theorems for Colored Sets

An Erdős-Ko-Rado-type theorem was established by Bollobás and Leader for q-signed sets and by Ku and Leader for partial permutations. In this paper, we establish an LYM-type inequality for partial permutations, and prove Ku and Leader’s conjecture on maximal k-uniform intersecting families of partial permutations. Similar results on general colored sets are presented.