On stars in caterpillars and lobsters

The family of all independent k-sets a graph containing fixed vertex v is called star and its center. Stars are interesting for their relation to Erdős–Ko–Rado graphs. Hurlbert Kamat conjectured that in trees the largest stars centered leaves. This conjecture was disproven independently by Baber, Borg, Feghali, Johnson, Thomas. In this paper we introduce tool bound size at certain vertices We use show caterpillars satisfy Kamat’s conjecture, centers lobsters either leaves or spinal degree 2.