论文标题
在签名三角形和六角形网格的色数上
On the chromatic numbers of signed triangular and hexagonal grids
论文作者
论文摘要
签名的图是一个简单的图形，具有两种类型的边缘。切换签名图的顶点$ v $对应于将每个边缘事件的类型更改为$ v $。 从签名的图形$ g $到另一个签名的图形$ h $的同构是一个映射$φ：v（g）\ rightarrow v（h）$，这样，在将$ g $的任何数量的顶点切换为$ g $的任何数量之后，$φ$映射$ g $的每个边缘的$ g $每个边缘在$ h $中的边缘上的边缘相同。签名图$ g $的色数$χ_s（g）$是最小签名的图形$ H $的订单，因此具有从$ g $到$ h $的同构。 我们表明，符号三角形网格的色度数最多为10，并且符号六角形网格的色数最多为4。
A signed graph is a simple graph with two types of edges. Switching a vertex $v$ of a signed graph corresponds to changing the type of each edge incident to $v$. A homomorphism from a signed graph $G$ to another signed graph $H$ is a mapping $φ: V(G) \rightarrow V(H)$ such that, after switching any number of the vertices of $G$, $φ$ maps every edge of $G$ to an edge of the same type in $H$. The chromatic number $χ_s(G)$ of a signed graph $G$ is the order of a smallest signed graph $H$ such that there is a homomorphism from $G$ to $H$. We show that the chromatic number of signed triangular grids is at most 10 and the chromatic number of signed hexagonal grids is at most 4.
