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On subdivisions of oriented cycles in Hamiltonian digraphs with small chromatic number | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 12 مرداد 1403 اصل مقاله (348.5 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2024.29517.2036 | ||
| نویسندگان | ||
| Salman Ghazal* 1، 2، 3؛ Sara Tfaili1، 2 | ||
| 1Department of Mathematics and Physics, Lebanese International University, LIU, Beirut, Lebanon | ||
| 2Department of Mathematics and Physics, The International University of Beirut, BIU, Beirut, Lebanon | ||
| 3Department of Mathematics, Faculty of Sciences I, Lebanese University, Beirut, Lebanon | ||
| چکیده | ||
| Cohen et al. conjectured that for each oriented cycle $C$, there is a smallest positive integer $f(C)$ such that every $f(C)$-chromatic strong digraph contains a subdivision of $C$. Let $C$ be an oriented cycle on $n$ vertices. For the class of Hamiltonian digraphs, El Joubbeh proved that $f(C)\leq 3n$. In this paper, we improve El Joubbeh's result by showing that $f(C)\leq 2n$ for the class of Hamiltonian digraphs. | ||
| کلیدواژه‌ها | ||
| Oriented cycle؛ Hamiltonian؛ Chromatic number؛ Subdivision | ||
| مراجع | ||
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[11] B. Roy, Nombre chromatique et plus longs chemins d’un graphe, Revue Fran¸caise D’Informatique Et De Recherche Opérationnelle 1 (1967), no. 5, 129–132. | ||
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