06121521

j

06121521 Nagy, Zolt\'an L\'or\'ant \"Ozkahya, Lale Patk\'os, Bal\'azs Vizer, M\'at\'e On the ratio of maximum and minimum degree in maximal intersecting families. Discrete Math. 313, No. 2, 207-211 (2013). 2013 Elsevier Science B.V. (North-Holland), Amsterdam EN intersecting families maximum and minimum degree blocking sets

doi:10.1016/j.disc.2012.10.007

Summary: To study how balanced or unbalanced a maximal intersecting family $\cal F \subseteq \binom{[n]}{r}$ is we consider the ratio $\cal R(\cal F)=\frac {\Delta (\cal F)}{\delta (\cal F)}$ of its maximum and minimum degree. We determine the order of magnitude of the function $m(n,r)$, the minimum possible value of $\cal R(\cal F)$, and establish some lower and upper bounds on the function $M(n,r)$, the maximum possible value of $\cal R(\cal F)$. To obtain constructions that show the bounds on $m(n,r)$ we use a theorem of Blokhuis on the minimum size of a non-trivial blocking set in projective planes.