article published yes Zdeněk Dvořák author Benjamin Moore author 6dc1a1be-bf1c-11ed-8d2b-d044840f49d6 Michaela Seifrtová author Robert Šámal author MaKw department We consider the 4-precoloring extension problem in planar near-Eulerian- triangulations, i.e., plane graphs where all faces except possibly for the outer one have length three, all vertices not incident with the outer face have even degree, and exactly the vertices incident with the outer face are precolored. We give a necessary topological condition for the precoloring to extend, and give a complete characterization when the outer face has length at most five and when all vertices of the outer face have odd degree and are colored using only three colors. https://research-explorer.ista.ac.at/download/19879/19887/2025_EuropJournCombinatorics_Dvorak.pdf application/pdfno Elsevier2025 eng 0195-6698 2312.13061 00144306140000110.1016/j.ejc.2025.104138 127 Dvořák Z, Moore B, Seifrtová M, Šámal R. 2025. Precoloring extension in planar near-Eulerian-triangulations. European Journal of Combinatorics. 127, 104138. Dvořák, Zdeněk, Benjamin Moore, Michaela Seifrtová, and Robert Šámal. “Precoloring Extension in Planar Near-Eulerian-Triangulations.” <i>European Journal of Combinatorics</i>. Elsevier, 2025. <a href="https://doi.org/10.1016/j.ejc.2025.104138">https://doi.org/10.1016/j.ejc.2025.104138</a>. Dvořák Z, Moore B, Seifrtová M, Šámal R. Precoloring extension in planar near-Eulerian-triangulations. <i>European Journal of Combinatorics</i>. 2025;127. doi:<a href="https://doi.org/10.1016/j.ejc.2025.104138">10.1016/j.ejc.2025.104138</a> Z. Dvořák, B. Moore, M. Seifrtová, and R. Šámal, “Precoloring extension in planar near-Eulerian-triangulations,” <i>European Journal of Combinatorics</i>, vol. 127. Elsevier, 2025. Z. Dvořák, B. Moore, M. Seifrtová, R. Šámal, European Journal of Combinatorics 127 (2025). Dvořák, Z., Moore, B., Seifrtová, M., &#38; Šámal, R. (2025). Precoloring extension in planar near-Eulerian-triangulations. <i>European Journal of Combinatorics</i>. Elsevier. <a href="https://doi.org/10.1016/j.ejc.2025.104138">https://doi.org/10.1016/j.ejc.2025.104138</a> Dvořák, Zdeněk, et al. “Precoloring Extension in Planar Near-Eulerian-Triangulations.” <i>European Journal of Combinatorics</i>, vol. 127, 104138, Elsevier, 2025, doi:<a href="https://doi.org/10.1016/j.ejc.2025.104138">10.1016/j.ejc.2025.104138</a>. 198792025-06-23T13:54:46Z2025-09-30T13:42:59Z