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arXiv · 1910.06201

Graphs in which the Maxine heuristic produces a maximum independent set

Benjamin Lantz
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Abstract

The residue of a graph is the number of zeros left after iteratively applying the Havel-Hakimi algorithm to its degree sequence. Favaron, Mah\'{e}o, and Sacl\'{e} showed that the residue is a lower bound on the independence number. The Maxine heuristic reduces a graph to an independent set of size $M$. It has been shown that given a graph $G$, $M$ is bounded between the independence number and the residue of a graph for any application of the Maxine heuristic. We improve upon a forbidden subgraph classification of graphs such that $M$ is equal to the independence number given by Barrus and Molnar in 2015.

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Benjamin Lantz. 2019-10-14. Graphs in which the Maxine heuristic produces a maximum independent set. https://arxiv.org/abs/1910.06201

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