Characterization of 4-critical triangle-free toroidal graphs
نویسندگان
چکیده
We give an exact characterization of 3-colorability triangle-free graphs drawn in the torus, form 186 “templates” (graphs with certain faces filled by arbitrary quadrangulations) such that a graph from this class is not 3-colorable if and only it contains subgraph matching one templates. As consequence, we show every torus edge-width at least six 3-colorable, key property used efficient algorithm for toroidal graphs.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2022
ISSN: ['0095-8956', '1096-0902']
DOI: https://doi.org/10.1016/j.jctb.2022.01.008