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The Chen-Lawrencenko Conjectures on Cyclic Colorations

Combinatorics · posed by Beifang Chen, Serge Lawrencenko, 1999 · disproved

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Statement

A cyclic coloration of a triangulation of a closed 2-manifold gives the faces around every vertex distinct colors. Chen and Lawrencenko made two conjectures about the cyclic chromatic number of minimal triangulations in 1999. Their second is proved here and their first disproved.

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. proof attempt · #1

    John M. Campbell, using GPT-5.6 Pro

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai co developed
    — a person and a model developed the result together.

    "We succeed, based on our extensive interactions with GPT-5.6 Pro, in proving and disproving, respectively, Chen and Lawrencenko's second and first conjectures." The acknowledgement places the model in the exploratory and proof-development stages, with all suggestions substantially revised, corrected and independently verified by the author.

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