Spanning 3-Ended Trees in Almost Claw-Free Graphs

Abstract EN

We prove that if G is a k -connected ( k ≥ 2 ) almost claw-free graph of order n and σ k + 3 ( G ) ≥ n + 2 k - 2 , then G contains a spanning 3-ended tree, where σ k ( G ) = min { ∑ v ∈ S deg ( v ) : S is an independent set of G with S = k } .