完全3-一致超图K_n~((3))的哈密顿圈分解

基于王建方和李东给出的超图哈密顿圈的定义和Katona-Kierstead给出的超图哈密顿链的定义,近年来,国内外学者对一致超图的哈密顿圈分解的研究有一系列结果.特别是Bailey-Stevens和Meszka-Rosa研究了完全3-一致超图K_n~((3))的哈密顿圈分解,得到了n=6k+1,6k+2(k=1,2,3,4,5)的哈密顿圈分解.本文在吉日木图提出的边划分方法的基础上继续研究,得到了完全3-一致超图K_n~((3))的哈密顿圈分解的算法,由此得到了n=6k+2,6k+4(k=1,2,3,4,5,6,7),n=6k+5(k=1,2,3,4,5,6)时的圈分解.这一结果将Meszka-Rosa关于K_n~((3))的哈密顿圈分解结果从n≤32提高到了n≤46(n≠43).

Decomposing the Complete 3-Uniform Hypergraphs Kn(3) Into Hamiltonian Cycles

Based on the definition of a Hamiltonian cycle gived by Janfang Wang and Tony Lee, and the definition of a Hamiltonian chain gived by Katona–Kierstead in a uniform hypergraph, recently, many domestic and foreign researchers studied the hamiltonian cycle decomposition of the uniform hypergraphs K_n⁽³⁾, and obtained a series of results. Especially, Bailey–Stevens and Meszka–Rosa studied the hamiltonian cycle decomposition of the complete 3-uniform hypergraphs K_n⁽³⁾, showed the result of hamiltonian cycle decomposition of K_n⁽³⁾ for n = 6k + 1, 6k + 2 (k= 1, 2, 3, 4, 5). In this paper, using the methods of edge-partition proposed by Jirimutu, we will continue study Hamiltonian decomposition of the complete 3-uniform hypergraphs K_n⁽³⁾, design an algorithm of Hamiltonian decompositions of K_n⁽³⁾, and use the algorithm, we show the result of hamiltonian cycle decomposition of K_n⁽³⁾ for n = 6k + 2, 6k + 4 (k= 1, 2, 3, 4, 5, 6, 7), n = 6k+5 (k= 1, 2, 3, 4, 5, 6). These results improve results of Hamiltonian decompositions from all admissible n ≤ 32 (Meszka–Rosa's paper) to all admissible n ≤ 46 and n = 43.