Neighborhood fixed pendant vertices
Authors: S. E. Anacker and G. N. Robertson
Journal: Trans. Amer. Math. Soc. 266 (1981), 115-128
MSC: Primary 05C60; Secondary 05C25
MathSciNet review: 613788
Abstract: If is pendant in , then denotes the unique vertex of adjacent to . Such an is said to be neighborhood-fixed whenever is fixed by . It is shown that if is not a tree and has a pendant vertex, but no *-fixed pendant vertex, then there is a subgraph of such that for some , where is the maximum number of edges in a tree rooted in .
Keywords: Reducible partitions, neighborhood fixed pendant vertices
Article copyright: © Copyright 1981 American Mathematical Society