Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8903011 | Discrete Mathematics | 2018 | 5 Pages |
Abstract
A family A of sets is said to be intersecting if every two sets in A intersect. Two families A and B are said to be cross-intersecting if each set in A intersects each set in B. For a positive integer n, let [n]={1,â¦,n} and Sn={Aâ[n]:1âA}. We extend the ErdÅs-Ko-Rado Theorem by showing that if A and B are non-empty cross-intersecting families of subsets of [n], A is intersecting, and a0,a1,â¦,an,b0,b1,â¦,bn are non-negative real numbers such that ai+biâ¥anâi+bnâi and anâiâ¥bi for each iâ¤nâ2, then âAâAa|A|+âBâBb|B|â¤âAâSna|A|+âBâSnb|B|.For a graph G and an integer râ¥1, let IG(r) denote the family of r-element independent sets of G. Inspired by a problem of Holroyd and Talbot, Feghali, Johnson and Thomas conjectured that if r
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Peter Borg,