Planar digraphs of digirth four are 2-colourable
نویسندگان
چکیده
Neumann-Lara conjectured in 1985 that every planar digraph with digirth at least three is 2-colourable, meaning that the vertices can be 2-coloured without creating any monochromatic directed cycles. We prove a relaxed version of this conjecture: every planar digraph of digirth at least four is 2-colourable.
منابع مشابه
Planar Digraphs of Digirth Five Are 2-Colorable
Neumann-Lara (1985) and Škrekovski conjectured that every planar digraph with digirth at least three is 2-colorable, meaning that the vertices can be 2-colored without creating any monochromatic directed cycles. We prove a relaxed version of this conjecture: every planar digraph of digirth at least five is 2-colorable. The result also holds in the setting of list colorings.
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عنوان ژورنال:
- SIAM J. Discrete Math.
دوره 31 شماره
صفحات -
تاریخ انتشار 2017