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On subdivisions of oriented cycles in Hamiltonian digraphs with small chromatic number | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 1، دوره 11، شماره 2، شهریور 2026، صفحه 307-314 اصل مقاله (348.25 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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[7] M. El Joubbeh and S. Ghazal, Existence of paths with t blocks in $k(t)$-chromatic, Discrete Appl. Math. 342 (2024), 381–384 . https://doi.org/10.1016/j.dam.2023.09.025
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[10] D.A. Mniny and S. Ghazal, Remarks on the subdivisions of bispindles and two-blocks cycles in highly chromatic digraphs, arXiv preprint arXiv:2010.10787 (2020).
[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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