The star-arboricity of the complete regular multipartite graphs

Abstract A subgraph H of a graph G is called a star-subgraph if each component of H is a star. The star-arboricity of G , denoted by sa( G ), is the minimum number of star-subgraphs that partition the edges of G . In this paper we show that sa( G ) is ⌈ r ⧸2⌉ + 1 or ⌈ r ⧸2⌉ + 2 for the complete r -regular multipartite graph G . And if r is even or if r is sufficiently larger than the number of partite sets, then sa( G ) is ⌈ r ⧸2⌉ + 2.