Article Dans Une Revue SIAM Journal on Discrete Mathematics Année : 2022

Square coloring planar graphs with automatic discharging

Résumé

The discharging method is a powerful proof technique, especially for graph coloring problems. Its major downside is that it often requires lengthy case analyses, which are sometimes given to a computer for verification. However, it is much less common to use a computer to actively look for a discharging proof. In this paper, we use a Linear Programming approach to automatically look for a discharging proof. While our system is not entirely autonomous, we manage to make some progress towards Wegner's conjecture for distance-2 coloring of planar graphs, by showing that 12 colors are sufficient to color at distance 2 every planar graph with maximum degree 4.

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hal-04960763 , version 1 (21-02-2025)

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Nicolas Bousquet, Quentin Deschamps, Lucas de Meyer, Théo Pierron. Square coloring planar graphs with automatic discharging. SIAM Journal on Discrete Mathematics, 2022, 38 (1), pp.504-528. ⟨10.1137/22M1492623⟩. ⟨hal-04960763⟩
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