A Note on the Parallel Cleaning of Cliques
Alejandro Angeli Ayello, Margaret-Ellen Messinger
TL;DR
This paper disproves a previous conjecture and establishes a new upper bound for the minimum number of brushes needed to continually parallel clean a clique, advancing understanding of graph cleaning processes.
Contribution
It provides a counterexample to a prior conjecture and introduces a tighter upper bound for the brush number in clique cleaning.
Findings
Disproved a conjecture from 2010.
Established a new upper bound for brush number.
Enhanced understanding of parallel clique cleaning.
Abstract
We disprove a conjecture proposed in [Gaspers et al., Discrete Applied Mathematics, 2010] and provide a new upper bound for the minimum number of brushes required to continually parallel clean a clique.
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Taxonomy
Topicssemigroups and automata theory · Computability, Logic, AI Algorithms · Complexity and Algorithms in Graphs