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- W2890400938 abstract "Despite the existence of a proof of the 4-color theorem, it would seem that there is still more to learn about why any planar graph is 4-colorable. To that end, we take another look at the Birkhoff diamond and discover something new and intriguing: after an extensive search for (rare) Kempe-locked triangulations, we find a Birkhoff diamond subgraph in each one. We offer a heuristic argument as to why that result is not only reasonable but also to be expected and posit that the presence of a Birkhoff diamond is necessary to Kempe-locking. If that conjecture is true, it means that the Birkhoff diamond plays a double role in the matter of 4-colorability, simultaneously working for opposite sides of whether a given planar graph could possibly be a minimum counterexample." @default.
- W2890400938 created "2018-09-27" @default.
- W2890400938 creator A5066140569 @default.
- W2890400938 date "2018-09-08" @default.
- W2890400938 modified "2023-09-27" @default.
- W2890400938 title "The Birkhoff Diamond as Double Agent" @default.
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- W2890400938 hasPublicationYear "2018" @default.
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