4 research outputs found
Two sufficient conditions for graphs to admit path factors
Let be a set of connected graphs. Then a spanning subgraph
of is called an -factor if each component of is isomorphic
to some member of . Especially, when every graph in
is a path, is a path factor. For a positive integer , we write
. Then a -factor
means a path factor in which every component admits at least vertices. A
graph is called a -factor deleted graph if
admits a -factor for any with
. A graph is called a -factor critical
graph if has a -factor for any
with . In this paper, we present two degree conditions for graphs to be
-factor deleted graphs and
-factor critical graphs. Furthermore, we show that the
two results are best possible in some sense