Odd star decomposition of complete bipartite graphs
Purwanto Purwanto, Fryska Ayu Winanthi · AIP conference proceedings · 2020
Let G1, G2, G3,…, Gn be connected subgraph of G. If E(G) = E(G1)∪E(G2)∪ … ∪E(Gn) and E(Gi) ∩ E(Gj) = ø for any i ≠ j, then (G1, G2, G3,…, Gn) is a decomposition of G. The even star decomposition (S2, S4,…, S2t) of a complate bipartite graph Km,n, where Si 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 (S1, S3, S5,…, S2t-1) of a complete bipartite graph Km,n when 1 ≤ m ≤ 5.