Efficient maximum matching algorithms for trapezoid graphs

• Main Authors: Phan-Thuan Do, Ngoc-Khang Le, Van-Thieu Vu
• Format: Article
• Language: English
• Published: Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), Indonesia 2017-04-01
• Series: Electronic Journal of Graph Theory and Applications
• Subjects: trapezoid graphs, maximum matching
• Online Access: https://www.ejgta.org/index.php/ejgta/article/view/273

Trapezoid graphs are intersection graphs of trapezoids between two horizontal lines. Many NP-hard problems can be solved in polynomial time if they are restricted on trapezoid graphs. A matching in a graph is a set of pairwise disjoint edges, and a maximum matching is a matching of maximum size. In this paper, we first propose an $O(n(\log n)^3)$ algorithm for finding a maximum matching in trapezoid graphs, then improve the complexity to $O(n(\log n)^2)$. Finally, we generalize this algorithm to a larger graph class, namely $k$-trapezoid graphs. To the best of our knowledge, these are the first efficient maximum matching algorithms for trapezoid graphs.