an:06590866
Zbl 1339.05305
Dyer, Danny; Haghshenas, Sadegheh; Shalaby, Nabil
Constructing the spectrum of packings and coverings for the complete graph with stars with up to five edges
EN
Graphs Comb. 32, No. 3, 943-961 (2016).
00355664
2016
j
05C70
packing; covering; leave graph; excess graph
Summary: The packing and covering problems have been considered for several classes of graphs. For instance, \textit{D. Bryant} and \textit{D. Horsley} [J. Comb. Theory, Ser. B 98, No. 5, 1014--1037 (2008; Zbl 1162.05037)] have investigated the packing problem for paths and cycles, and the packing and covering problems for 3-cubes. The packing and covering problems were settled for stars 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); Ars Comb. 35, 33--64 (1993; Zbl 0796.05074)]. In this paper, for every possible leave graph (excess graph), we find a corresponding maximum packing (minimum covering) of the complete graph with stars with up to five edges.
Zbl 1162.05037; Zbl 0521.05053; Zbl 0608.05028; Zbl 0578.05013; Zbl 0796.05074