论文标题
奇数图的弧形着色汉密尔顿
Arc coloring of odd graphs for hamiltonicity
论文作者
论文摘要
引入了双重图形的弧形，并可能应用于工业化学，分子生物学，细胞神经科学等。在这里，我们在某些非双层图中处理弧形着色。实际上，对于$ 1 <k \ in \ mathbb {z} $，我们发现奇数图$ o_k $具有弧分分解，颜色为$ 0,1，\ ldots，k $，因此每个边缘的两个弧的颜色的总和等于$ k $。这适用于在最近构建的$ o_k $中的均匀2因子和汉密尔顿周期中的$ o_k $以及其双层覆盖图中的汉密尔顿周期中分析这种弧因子化的影响。
Coloring the arcs of biregular graphs was introduced with possible applications to industrial chemistry, molecular biology, cellular neuroscience, etc. Here, we deal with arc coloring in some non-bipartite graphs. In fact, for $1<k\in\mathbb{Z}$, we find that the odd graph $O_k$ has an arc factorization with colors $0,1,\ldots,k$ such that the sum of colors of the two arcs of each edge equals $k$. This is applied to analyzing the influence of such arc factorizations in recently constructed uniform 2-factors in $O_k$ and in Hamilton cycles in $O_k$ as well as in its double covering graph known as the middle-levels graph $M_k$.
