3-coloring triangle-free planar graphs with a precolored 9-cycle

Bernard Lidick\'y; Ilkyoo Choi; Jan Ekstein; P\v{r}emysl Holub

arxiv: 1709.09428 · v1 · pith:SFDZH3NVnew · submitted 2017-09-27 · 🧮 math.CO

3-coloring triangle-free planar graphs with a precolored 9-cycle

Ilkyoo Choi , Jan Ekstein , P\v{r}emysl Holub , Bernard Lidick\'y This is my paper

classification 🧮 math.CO

keywords coloringcycleplanartriangle-freecharacterizeextendextendsgiven

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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.

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3-coloring triangle-free planar graphs with a precolored 9-cycle

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