Complexity of diameter on AT-free graphs is linear
Data Structures and Algorithms
2023-03-24 v4 Combinatorics
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.
Cite
@article{arxiv.2209.00110,
title = {Complexity of diameter on AT-free graphs is linear},
author = {Oleksiy Al-saadi and Jitender Deogun},
journal= {arXiv preprint arXiv:2209.00110},
year = {2023}
}
Comments
Problems with certain cases when determining the diameter at low diameter