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Planar Digraphs of Digirth Five Are 2‐Colorable |
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| Authors: | Ararat Harutyunyan Bojan Mohar |
| Affiliation: | 1. INSTITUT DE MATHéMATIQUES DE TOULOUSE, UNIVERSITé TOULOUSE III (PAUL SABATIER), FRANCEContract grant sponsor: Digiteo postdoctoral scholarship.;2. DEPARTMENT OF MATHEMATICS, SIMON FRASER UNIVERSITY, BURNABY, BC, CANADAContract grant sponsor: NSERC Discovery Grant (Canada);3. contract grant sponsor: Canada Research Chair program;4. contract grant number: Research Grant P1–0297 of ARRS (Slovenia). On leave from: IMFM, and FMF, Department of Mathematics, University of Ljubljana, Ljubljana, Slovenia. |
| Abstract: | Neumann‐Lara (1985) and ?krekovski 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. |
| Keywords: | planar digraph digraph chromatic number dichromatic number discharging |