Complexity of diameter on AT-free graphs is linear

08/31/2022

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by   Oleksiy Al-Saadi, et al.

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We exploit properties of dominating pair sets (polar pairs) in asteroidal triple-free (AT-free) graphs to compute diameter in linear-time. As a consequence, we improve the best known running time of the well-known graph theoretical problems of finding a simplicial vertex and triangle recognition in general graphs to O(n^2).