论文标题
特殊Digraph类的弱点色索引
Weak-odd chromatic index of special digraph classes
论文作者
论文摘要
给出一个digraph $ d =（v（d），a（d））$，让$ \ partial^+_ d（v）= \ {vw | w \ in N^+_ d（v）\} $和$ \ partial^-_d（v）= \ {uv {uv | in n^-_ d（v）映射$φ：a（d）\ rightarrow [k] $称为弱odd $ k $ - edge $ d $，如果满足条件：对于v（d）$中的每个$ v \ in v（d）$，至少有一种颜色，每个颜色都有奇数的奇数，则每种非空的半级别的$ v $ $ v $。我们称最低整数$ k $为$ d $的弱odd色度指数。当限制为2种颜色时，请使用$ def（d）$表示$ d $的缺陷，这是不满足上述条件的$ d $中的最小顶点。在本文中，我们给出了关于弱odd色度指数以及半完整的挖掘和扩展比赛的缺陷的描述性表征，这将比赛的结果推广到更广泛的阶级。我们启动了对挖掘的弱odd边缘覆盖的研究。
Give a digraph $D=(V(D),A(D))$, let $\partial^+_D(v)=\{vw|w\in N^+_D(v)\}$ and $\partial^-_D(v)=\{uv|u\in N^-_D(v)\}$ be semi-cuts of $v$. A mapping $φ:A(D)\rightarrow [k]$ is called a weak-odd $k$-edge coloring of $D$ if it satisfies the condition: for each $v\in V(D)$, there is at least one color with an odd number of occurrences on each non-empty semi-cut of $v$. We call the minimum integer $k$ the weak-odd chromatic index of $D$. When limit to 2 colors, use $def(D)$ to denote the defect of $D$, the minimum number of vertices in $D$ at which the above condition is not satisfied. In this paper, we give a descriptive characterization about the weak-odd chromatic index and the defect of semicomplete digraphs and extended tournaments, which generalize results of tournaments to broader classes. And we initiated the study of weak-odd edge covering on digraphs.
