A Linear Algorithm for Computing of a Minimum Weight Maximal Induced Matching in an Edge-Weighted Tree

Lepin, V. V.

doi:10.1016/j.endm.2006.06.019

Cited by 6 publications

(2 citation statements)

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“…However, in such a class G, it is still interesting to find structural characterizations of wellindumatched graphs which can possibly lead to simpler recognition algorithms. This is the case for trees as both MIM and MMIM can be solved in linear time by the algorithms given in [19] and [25], respectively. In Section 3, we provide a simple characterization of well-indumatched trees which provides a much simpler linear time recognition algorithm.…”

Section: Complexity Of Various Graph Problems In Gmentioning

confidence: 99%

“…In [19], a linear time algorithm for finding the maximum size of an induced matching in a tree is presented. Besides, a linear time algorithm is given for finding the size of a minimum maximal induced matching in a tree in [25]. These two algorithms provide a linear time algorithm for recognizing whether a tree is well-indumatched.…”

Section: Characterization Of Well-indumatched Treesmentioning

confidence: 99%

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Well-indumatched Trees and Graphs of Bounded Girth

Akbari¹,

Ekim²,

Ghodrati³

et al. 2019

Preprint

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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 ≥ 9 and g = 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 ∈ {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.

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Section: Complexity Of Various Graph Problems In Gmentioning

confidence: 99%

Section: Characterization Of Well-indumatched Treesmentioning

confidence: 99%