Model
Digital Document
Publisher
Florida Atlantic University
Description
If T is a tree on n vertices, n 3, and if G is a connected graph such that dudvd u,v 2n for
every pair of distinct vertices of G, it has been conjectured that G must have a non-separating
copy of T. In this note, we prove this result for the special case in which dudv du,v 2n 2 for every
pair of distinct vertices of G, and improve this slightly for trees of diameter at least four and for
some trees of diameter three. We also characterize the graphs on at most 8 vertices with
dudvdu,v 7 for every pair of distinct vertices of G, and no non-separating copy of K_{1,3}
every pair of distinct vertices of G, it has been conjectured that G must have a non-separating
copy of T. In this note, we prove this result for the special case in which dudv du,v 2n 2 for every
pair of distinct vertices of G, and improve this slightly for trees of diameter at least four and for
some trees of diameter three. We also characterize the graphs on at most 8 vertices with
dudvdu,v 7 for every pair of distinct vertices of G, and no non-separating copy of K_{1,3}
Member of