The smallest 5-chromatic tournament
نویسندگان
چکیده
A coloring of a digraph is partition its vertex set such that each class induces with no directed cycles. k k -chromatic if the minimum number classes in partition, and oriented there at most one arc between pair vertices. Clearly, smallest complete on vertices, but determining order graphs challenging problem. It known alttext="2"> 2 encoding="application/x-tex">2 -, alttext="3"> 3 encoding="application/x-tex">3 - alttext="4"> 4 encoding="application/x-tex">4 have , alttext="7"> 7 encoding="application/x-tex">7 alttext="11"> 11 encoding="application/x-tex">11 respectively. In 1994, Neumann-Lara conjectured alttext="5"> 5 encoding="application/x-tex">5 graph has alttext="17"> 17 encoding="application/x-tex">17 We solve this conjecture show correct alttext="19"> 19 encoding="application/x-tex">19 .
منابع مشابه
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2023
ISSN: ['1088-6842', '0025-5718']
DOI: https://doi.org/10.1090/mcom/3887