# Sandi Klavžar: General d-position sets

Date of publication: 18. 1. 2021

Discrete mathematics seminar

Tuesday

19

January

Time:

10:15

Location:

Zoom

ID: 997 6207 6197
–
Password: 144896

**Tuesday, January 19th at 10.15 **

Join Zoom Meeting

https://uni-lj-si.zoom.us/j/99762076197?pwd=WGZXY29URFJ2cXZ0SkVLYWNGN0Z5dz09

Meeting ID: 997 6207 6197

Passcode: 144896

**Abstract.**The general

*d*-position number gp

_{d}(

*G*) of a graph

*G*is the cardinality of a largest set

*S*for which no three distinct vertices from

*S*lie on a common geodesic of length at most

*d*. This new graph parameter generalizes the well-studied general position number. In this talk, we will first give some results concerning the monotonic behavior of gp

_{d}(

*G*) with respect to the suitable values of

*d*. We will show that the decision problem concerning finding gp

_{d}(

*G*) is NP-complete for any value of

*d*. Then we have a look to infinite graphs. A structural characterization of general

*d*-position sets will be given. Some relationships with other topics including strong resolving graphs and dissociation sets will also be presented.

Based on a joint work with Douglas F. Rall and Ismael G. Yero.