### Abstract

We investigate terminal-pairability properties of complete graphs and improve the known bounds in two open problems. We prove that the complete graph $K_n$ on $n$ vertices is terminal-pairable if the maximum degree $\Delta$ of the corresponding demand multigraph $D$ is at most $2\lfloor\frac{n}{6}\rfloor-4$. We also verify the terminal-pairability property when the number of edges in $D$ does not exceed $2n-5$ and $\Delta\leq n-1$ holds.

Publication

Journal of Combinatorial Mathematics and Combinatorial Computing

*Dedicated to the memory of our friend, professor Ralph Faudree.*

Submitted in October, 2016. Appeared in the November 2018 issue of JCMCC (see the
Table of Contents.)

###### Mathematician

My research interests include Graph Theory, Computational Geometry, and Algorithms