Paper Info
Title
On The General Position Problem On Kneser Graphs
Abstract
In a graph G, a geodesic between two vertices x and y is a shortest path connecting x to y. A subset S of the vertices of G is in general position if no vertex of S lies on any geodesic between two other vertices of S. The size of a largest set of vertices in general position is the general position number that we denote by gp(G). Recently, Ghorbani et al. proved that for any k if n >= k(3) - k(2) + 2k - 2, then gp(Kn(n, k)) = ((n - 1)(k - 1)), where Kn(n, k) denotes the Kneser graph. We improve on their result and show that the same conclusion holds for n >= 2.5k - 0.5 and this bound is best possible. Our main tools are a result on cross-intersecting families and a slight generalization of Bollobas's inequality on intersecting set pair systems.
Year
DOI
Venue
2020
10.26493/1855-3974.1957.a0f
ARS MATHEMATICA CONTEMPORANEA
Keywords
DocType
Volume
General position problem, Kneser graphs, intersection theorems
Journal
18
Issue
ISSN
Citations 
2
1855-3966
0
PageRank 
References 
Authors
0.34
0
1
Name
Order
Citations
PageRank
Balázs Patkós18521.60