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arXiv · 2209.00110

Complexity of diameter on AT-free graphs is linear

Oleksiy Al-saadi·Jitender Deogun
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Abstract

We develop a linear time algorithm for finding the diameter of an asteroidal triple-free (AT-free) graph. Furthermore, we update the definition of polar pairs and develop new properties of polar pairs for (weak) dominating pair graphs. We prove that the problem of computing a simplicial vertex in a general graph can be accomplished in O(n^2) based on an existing reduction to the problem of finding diameter in an AT-free graph. We improve the best-known run-time complexities of several graph theoretical problems.

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Oleksiy Al-saadi, Jitender Deogun. 2022-08-31. Complexity of diameter on AT-free graphs is linear. https://arxiv.org/abs/2209.00110

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