Efficient maximum matching algorithms for trapezoid graphs

Phan-Thuan Do, Ngoc-Khang Le, Van-Thieu Vu


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.


trapezoid graphs, maximum matching

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DOI: http://dx.doi.org/10.5614/ejgta.2017.5.1.2


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