MathDB

5

Part of 1979 IMO Shortlist

Problems(1)

Find the maximal cardinality

Source: IMO LongList 1979 - P15

9/15/2010
Let n≥2n \geq 2 be an integer. Find the maximal cardinality of a set MM of pairs (j,k)(j, k) of integers, 1≤j<k≤n1 \leq j < k \leq n, with the following property: If (j,k)∈M(j, k) \in M, then (k,m)∉M(k,m) \not \in M for any m.m.
graph theorynumber theorymaximizationExtremal Graph TheoryExtremal combinatoricsIMO ShortlistIMO Longlist