{ 0 , 2 } -Degree free spanning forests in graphs

Let G be a graph and S be a set of non-negative integers. By an S -degree free spanning forest of G we mean a spanning forest of G with no vertex degree in S . In this paper we study the existence of { 0 , 2 } -degree free spanning forests in graphs. We show that if G is a graph with minimum degree at least 4, then there exists a { 0 , 2 } -degree free spanning forest. Moreover, we show that every 2-connected graph with maximum degree at least 5 admits a { 0 , 2 } -degree free spanning forest, and every 3-connected graph admits a { 0 , 2 } -degree free spanning forest.