Abstract:

A star-factor of a graph G is a spanning subgraph of G in which every component is a star. Kano and Saito (Discret Math 312: 2005–2008, 2012) showed that a graph G satisfying iso(G − S)  |S|/m for every S ⊂ V(G) contains a {K1,t : m  t  2m}-factor, where iso(G−S) denotes the number of isolated vertices in G − S. Then they conjectured that a graph G satisfying iso(G − S)  |S|/m for every S ⊂ V(G) actually contains a ({K1,t : m  t  2m −1} ∪ {K2m+1})-factor. In this paper, we show that this conjecture is true.

Key words: Star-factor ·, Component ·, Isolated vertex