Título: | Disproof of a conjecture of Neumann-Lara |
Autor(es): | LLANO PEREZ, BERNARDO OLSEN, MIKA |
Temas: | Torneos circulantes Número dicromático Desconexión acíclica |
Fecha: | 2017 |
Editorial: | Australia : Electronic Journal of Combinatorics |
Citation: | The Electronic Journal of Combinatorics, 24 (4) 2017 |
Resumen: | We disprove the following conjecture due to Victor Neumann-Lara: for every pair (r; s) of integers such that r > s > 2, there is an in nite set of circulant tournaments T such that the dichromatic number and the cyclic triangle free disconnection of T are equal to r and s, respectively. Let Fr;s denote the set of circulant tournaments T with dc(T) = r and w 3 (T) = s. We show that for every integer s > 4 there exists a lower bound b(s) for the dichromatic number r such that Fr;s = ; for every r < b(s). We construct an in nite set of circulant tournaments T such that dc(T) = b(s) and w 3(T) = s and give an upper bound B(s) for the dichromatic number r such that for every r > B(s) there exists an in nite set Fr;s of circulant tournaments. Some in nite sets Fr;s of circulant tournaments are given for b(s) < r < B(s). |
URI: | http://ilitia.cua.uam.mx:8080/jspui/handle/123456789/718 |
Aparece en las colecciones: | Artículos |
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Disproof of a conjecture of Neumann-Lara.pdf | 294.07 kB | Adobe PDF | Visualizar/Abrir |
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