The three-color conjecture for weak conflict-free vertex-to-vertex guarding

A simple polygon is a polygonal region whose boundary is a simple polygonal curve. In weak conflict-free vertex-to-vertex chromatic guarding, guards are placed at polygon vertices and a vertex is guarded when it sees a guard of a color that no other visible guard has.

Three-color guarding conjecture. Every simple polygon admits a weak conflict-free vertex-to-vertex chromatic guarding with at most 33 colors.

This conjecture concerns the number of colors needed for weak conflict-free visibility guarding. The source presents it as a suggestion from investigation rather than as a proved result; its resolution is left open.

Sources & referencesView supporting material

Primary source

Onur Çağırıcı, “Computational Aspects of Problems on Visibility and Disk Graph Representations”, arXiv:2111.00609 (2021).

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