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,...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.展开更多
文摘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.
