Well-indumatched Trees and Graphs of Bounded Girth [article]

S. Akbari, T. Ekim, A.H. Ghodrati, S. Zare
2019 arXiv   pre-print
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
more » ... y 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.
arXiv:1903.03197v2 fatcat:uqxica22f5fmzminvnjjk7za5y