Chain Graphs have Unbounded Readability
Abstract
A triangle-free graph
G
is called read-
k
when there exists a monotone Boolean formula
ϕ
whose variables are the vertices of
G
and whose minterms are precisely the edges of
G
, such that no variable occurs more than
k
times in
ϕ
. The smallest such
k
is called the readability of
G
. We exhibit a very simple class of bipartite chain graphs on
2n
vertices with readability
Ω(
logn
loglogn
−
−
−
−
−
−
√
)
.