r-EKR property for all spiders

Prove or disprove that every spider graph is r-EKR for every admissible r.

Background

The survey records positive results for several spider families, including uniform spiders in restricted ranges and arbitrary spiders in the stronger minimum-degree-center formulation under a specified spider ordering.

It then explicitly asks whether the full r-EKR property holds for all spiders, leaving the general case unresolved.