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arXiv · 2403.08210

Exact upper bounds for the minimum sizes of strong and weak separating path systems of cliques

George Kontogeorgiou·Maya Stein
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Abstract

We prove an upper bound of $n+9$ for the strong separation number of the complete graph $K_n$, and an upper bound of $n+1$ for its weak separation number. This improves on the previous best known bound of $(1+o(1))n$ for both cases.

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George Kontogeorgiou, Maya Stein. 2026-03-24. Exact upper bounds for the minimum sizes of strong and weak separating path systems of cliques. https://arxiv.org/abs/2403.08210

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