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Communication Dans Un Congrès Année : 2023

Cutting Barnette graphs perfectly is hard

Résumé

A perfect matching cut is a perfect matching that is also a cutset, or equivalently a perfect matching containing an even number of edges on every cycle. The corresponding algorithmic problem, Perfect Matching Cut, is known to be NP-complete in subcubic bipartite graphs [Le & Telle, TCS '22] but its complexity was open in planar graphs and in cubic graphs. We settle both questions at once by showing that Perfect Matching Cut is NP-complete in 3-connected cubic bipartite planar graphs or Barnette graphs. Prior to our work, among problems whose input is solely an undirected graph, only Distance-2 4-Coloring was known NP-complete in Barnette graphs. Notably, Hamiltonian Cycle would only join this private club if Barnette's conjecture were refuted.
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Dates et versions

hal-04292961 , version 1 (17-11-2023)

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  • HAL Id : hal-04292961 , version 1

Citer

Edouard Bonnet, Dibyayan Chakraborty, Julien Duron. Cutting Barnette graphs perfectly is hard. WG 2023, Jun 2023, Fribourg (Germany), Germany. ⟨hal-04292961⟩
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