正圆有向图中的弧不相交的Hamilton路和圈
发布时间：2018-11-03 17:54
【摘要】：2012年,Bang-Jensen和Huang(J.Combin.Theory Ser.B.2012,102:701-714)证明了2-弧强的局部半完全有向图可以分解为两个弧不相交的强连通生成子图当且仅当D不是偶圈的二次幂,并提出了任意3-强的局部竞赛图中包含两个弧不相交的Hamilton圈的猜想.主要研究正圆有向图中的弧不相交的Hamilton路和Hamilton圈,并证明了任意3-弧强的正圆有向图中包含两个弧不相交的Hamilton圈和任意4-弧强的正圆有向图中包含一个Hamilton圈和两个Hamilton路,使得它们两两弧不相交.由于任意圆有向图一定是正圆有向图,所得结论可以推广到圆有向图中.又由于圆有向图是局部竞赛图的子图类,因此所得结论说明对局部竞赛图的子图类 圆有向图,Bang-Jensen和Huang的猜想成立.
[Abstract]:In 2012, Bang-Jensen and Huang (J.Combin.Theory Ser.B.2012,102:701-714) proved that a locally semi-completely directed graph with 2-arc strength can be decomposed into two strongly connected generated subgraphs with disjoint arcs if and only if D is not a second power of even cycles. The conjecture of any 3-strong local tournaments containing two arc-disjoint Hamilton cycles is also given. In this paper, the Hamilton paths and Hamilton cycles with disjoint arcs in positive circular digraphs are studied, and it is proved that any 3-arc strong positive circular digraphs contain two Hamilton cycles with disjoint arcs and one Hamilton cycle and two Hamilton paths in any 4-arc strong positive circular digraphs. So that the two arcs do not intersect. Since an arbitrary circular digraph must be a positive circular digraph, the results obtained can be extended to a circular digraph. Since circular digraphs are subgraphs of local tournaments, the results show that the conjecture of Bang-Jensen and Huang is true for subgraphs of local tournaments.
【作者单位】： 山西大学数学科学学院;
【基金】：国家自然科学基金(11401353) 山西省自然科学基金(2016011005)
【分类号】：O157.5
[Abstract]:In 2012, Bang-Jensen and Huang (J.Combin.Theory Ser.B.2012,102:701-714) proved that a locally semi-completely directed graph with 2-arc strength can be decomposed into two strongly connected generated subgraphs with disjoint arcs if and only if D is not a second power of even cycles. The conjecture of any 3-strong local tournaments containing two arc-disjoint Hamilton cycles is also given. In this paper, the Hamilton paths and Hamilton cycles with disjoint arcs in positive circular digraphs are studied, and it is proved that any 3-arc strong positive circular digraphs contain two Hamilton cycles with disjoint arcs and one Hamilton cycle and two Hamilton paths in any 4-arc strong positive circular digraphs. So that the two arcs do not intersect. Since an arbitrary circular digraph must be a positive circular digraph, the results obtained can be extended to a circular digraph. Since circular digraphs are subgraphs of local tournaments, the results show that the conjecture of Bang-Jensen and Huang is true for subgraphs of local tournaments.
【作者单位】： 山西大学数学科学学院;
【基金】：国家自然科学基金(11401353) 山西省自然科学基金(2016011005)
【分类号】：O157.5
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