论文标题
部分可观测时空混沌系统的无模型预测
Conflict-free incidence coloring of outer-1-planar graphs
论文作者
论文摘要
图$ g $的发生率是顶点边对$（v，e）$，因此$ v $是$ e $的发病率。 A conflict-free incidence coloring of a graph is a coloring of the incidences in such a way that two incidences $(u,e)$ and $(v,f)$ get distinct colors if and only if they conflict each other, i.e.,(i) $u=v$, (ii) $uv$ is $e$ or $f$, or (iii) there is a vertex $w$ such that $uw=e$ and $vw=f$.图表的所有无冲突发射率颜色中使用的最小颜色数量是无冲突的发射率色数。如果可以在平面中绘制图形，则图形为外1平面，使顶点在外部边界上，并且每个边缘最多一次交叉。在本文中，我们表明，具有最高度$δ$的外部1平面图的无冲突发生率是$2δ$或$2δ+1 $，除非该图是三个顶点上的一个周期，并且所有outer-1-planar图带有冲突的无冲突的变色率$2Δ$或$2δ$或$2δ+1 $ $。给出了一种有效的算法，用于构建连接的外1平面图的最佳无冲突发射率着色。
An incidence of a graph $G$ is a vertex-edge pair $(v,e)$ such that $v$ is incidence with $e$. A conflict-free incidence coloring of a graph is a coloring of the incidences in such a way that two incidences $(u,e)$ and $(v,f)$ get distinct colors if and only if they conflict each other, i.e.,(i) $u=v$, (ii) $uv$ is $e$ or $f$, or (iii) there is a vertex $w$ such that $uw=e$ and $vw=f$. The minimum number of colors used among all conflict-free incidence colorings of a graph is the conflict-free incidence chromatic number. A graph is outer-1-planar if it can be drawn in the plane so that vertices are on the outer-boundary and each edge is crossed at most once. In this paper, we show that the conflict-free incidence chromatic number of an outer-1-planar graph with maximum degree $Δ$ is either $2Δ$ or $2Δ+1$ unless the graph is a cycle on three vertices, and moreover, all outer-1-planar graphs with conflict-free incidence chromatic number $2Δ$ or $2Δ+1$ are completely characterized. An efficient algorithm for constructing an optimal conflict-free incidence coloring of a connected outer-1-planar graph is given.
