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Well-indumatched trees and graphs of bounded girth

Akbari, S ; Sharif University of Technology | 2023

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  1. Type of Document: Article
  2. Publisher: University of Queensland , 2023
  3. Abstract:
  4. A graph G is called well-indumatched if all of its maximal induced match-ings have the same size. In this paper, we characterize all well-indumatch-ed trees. We provide a linear time algorithm to decide whether a tree is well-indumatched or not. Then, we characterize minimal well-indu-matched 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. © The author(s)
  5. Keywords:
  7. Source: Australasian Journal of Combinatorics ; Volume 85 , 2023 , Pages 61-81 ; 10344942 (ISSN)
  8. URL: https://ajc.maths.uq.edu.au/pdf/85/ajc_v85_p061.pdf