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The hamiltonicity and pancyclicity of split graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 03 تیر 1405 | ||
| نوع مقاله: Special issue of CCO to honor Odile Favaron | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2026.31342.2822 | ||
| نویسندگان | ||
| Junqing Cai1، 2؛ Hao Li* 3؛ Zhiyi Jiang1 | ||
| 1School of Mathematical Science, Tianjin Normal University, Tianjin 300387, China | ||
| 2Institute of Mathematics and Interdisciplinary Sciences, Tianjin Normal University, Tianjin 300387, China | ||
| 3Laboratoire Interdisciplinaire des Sciences du Numerique CNRS-Universite Paris-Saclay, Orsay 91405, France | ||
| چکیده | ||
| A split graph is a graph whose vertex set can be partitioned into two disjoint subsets (either of which may be empty) such that one subset induces a clique and the other induces an independent set. Regarding the hamiltonicity of such graphs, Dai et al. [Discrete Math. 345 (2022), 112826] conjectured that every $r$-connected $K_{1, r+1}$-free split graph is hamiltonian. In this paper, we provide a partial verification of this conjecture for the case $r=4$. Precisely, we show that every $4$-connected $\{K_{1,5}, K_{1,5}+e\}$-free split graph is hamiltonian. Furthermore, we address Bondy’s meta-conjecture proposed in 1971, which asserts that almost any nontrivial condition guaranteeing a graph to be hamiltonian also implies the graph to be pancyclic, except for a small number of well-characterized exceptional graphs. We prove that this meta-conjecture holds for split graphs. | ||
| کلیدواژهها | ||
| {K_(1؛ 5)؛ K_(1؛ 5) + e}-free graphs | ||
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