Odd Star Decomposition of Complete Bipartite Graphs

摘要

Let G_1, G_2, G_3,..., G_n be connected subgraph of G. If E(G) = E(G_1) UE(G_2) U ... UE(G_n) and E(G_i) ∩ E(G_j) = ? for any i ≠ j, then (G_1,G_2,G_3, ...,G_n) is a decomposition of G. The even star decomposition (S_2,S_4,...,S_(2t)) of a complate bipartite graph K_(m,n), where S_i is a star with i vertices of degree 1, has been studied by Merley and Goldy in 2016. In this paper we study an odd star decomposition (S_1, S_3, S_5,...,S_(2t-1)) of a complete bipartite graph K_(m,n) when 1 ≤ m ≤ 5.