Erdös-Ko-Rado from intersecting shadows

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...

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

Note Erdős–Ko–Rado from intersecting shadows

A set system is called t-intersecting if every two members meet each other in at least t elements. Katona determined the minimum ratio of the shadow and the size of such families and showed that the Erdős– Ko–Rado theorem immediately follows from this result. The aim of this note is to reproduce the proof to obtain a slight improvement in the Kneser graph. We also give a brief overview of corre...

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...

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.