The spectrum of optimal excess graphs for trees with up to four edges

Abstract

In 1978, Huang and Rosa solved the spectrum problem for decomposition for trees with up to eight edges. Also, the packing and covering problems were settled for trees with up to six edges by Roditty. In this paper, we find the spectrum of excess graphs for trees with up to four edges. Moreover, we use new techniques in our proofs and state lemmas that will be useful for generalizing our result for trees with higher number of edges. c