3-coloring Triangle-free Planar Graphs with a Precolored 8-cycle
نویسندگان
چکیده
Let G be a planar triangle-free graph and let C be a cycle in G of length at most 8. We characterize all situations where a 3-coloring of C does not extend to a proper 3-coloring of the whole graph.
منابع مشابه
3-Coloring Triangle-Free Planar Graphs with a Precolored 9-Cycle
Given a triangle-free planar graph G and a 9-cycle C in G, we characterize situations where a 3-coloring of C does not extend to a proper 3-coloring of G. This extends previous results when C is a cycle of length at most 8. Disciplines Mathematics Comments Choi, Ilkyoo, Jan Ekstein, Přemysl Holub, and Bernard Lidický. "3-coloring triangle-free planar graphs with a precolored 9-cycle." 68 Europe...
متن کامل3-coloring triangle-free planar graphs with a precolored
5 Given a triangle-free planar graph G and a cycle C of length 9 in G, we characterize 6 all situations where a 3-coloring of C does not extend to a proper 3-coloring of G. This 7 extends previous results for the length of C up to 8. 8
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متن کاملFine structure of 4-critical triangle-free graphs III. General surfaces
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ورودعنوان ژورنال:
- Journal of Graph Theory
دوره 80 شماره
صفحات -
تاریخ انتشار 2015