Spanning $$k$$ k -Forests with Large Components in $$K_{1,k+1}$$ K 1 , k + 1 -Free Graphs

Abstract

For an integer $$k$$k with $$k \ge 2$$k?2, a $$k$$k-tree (resp. a $$k$$k-forest) is a tree (resp. forest) with maximum degree at most $$k$$k. In this paper, we show that for any integer $$k$$k with $$k \ge 3$$k?3, any connected $$K_{1,k+1}$$K1,k+1-free graph has a spanning $$k$$k-tree or a spanning $$k$$k-forest with only large components.