an:07195757
Zbl 1439.05135
Dyer, Danny; Haghshenas, Sadegheh; Shalaby, Nabil
The spectrum of optimal excess graphs for trees with up to four edges
EN
AKCE Int. J. Graphs Comb. 16, No. 3, 272-279 (2019).
00448797
2019
j
05C50
covering; excess graph; design
Summary: \textit{C. Huang} and \textit{A. Rosa} [Ars Comb. 5, 23--63 (1978; Zbl 0418.05041)] 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 \textit{Y. Roditty} [J. Comb. Theory, Ser. A 35, 213--243 (1983; Zbl 0521.05053); Int. J. Math. Math. Sci. 9, 277--282 (1986; Zbl 0608.05028); Ars Comb. 19, 81--93 (1985; Zbl 0578.05013)]. 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.
Zbl 0418.05041; Zbl 0521.05053; Zbl 0608.05028; Zbl 0578.05013