1 research outputs found
Well-indumatched Trees and Graphs of Bounded Girth
A graph G is called well-indumatched if all of its maximal induced matchings
have the same size. In this paper we characterize all well-indumatched trees.
We provide a linear time algorithm to decide if a tree is well-indumatched or
not. Then, we characterize minimal well-indumatched graphs of girth at least 9
and show subsequently that for an odd integer g greater than or equal to 9 and
different from 11, there is no well-indumatched graph of girth g. On the other
hand, there are infinitely many well-indumatched unicyclic graphs of girth k,
where k is in {3, 5, 7} or k is an even integer greater than 2. We also show
that, although the recognition of well-indumatched graphs is known to be
co-NP-complete in general, one can recognize in polynomial time
well-indumatched graphs where the size of maximal induced matchings is fixed