Proper orientations and proper chromatic number
نویسندگان
چکیده
The proper orientation number χ→(G) of a graph G is the minimum k such that there exists an edges with all vertex-outdegrees at most and for any adjacent vertices, outdegrees are different. Two major conjectures about resolved. First it shown, planar 14. Secondly, shown every graph, , where r=χ(G) usual chromatic maximum average degree taken over subgraphs G. Several other related results derived. Our proofs based on novel notion fractional orientations.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2023
ISSN: ['0095-8956', '1096-0902']
DOI: https://doi.org/10.1016/j.jctb.2023.02.003