论文标题
在某些类图的签名色数上
On the signed chromatic number of some classes of graphs
论文作者
论文摘要
签名的图形$（g，σ）$是图$ g $，以及函数$σ：e（g）\ to \ {+{+， - \} $。签名图的封闭步行是正（分别，负），如果它具有均匀（分别，奇数）的负边数，计数重复。 （简单）签名的图与另一个签名图的同态是一个顶点映射，可保留封闭步行的邻接和迹象。签名的图形$（g，σ）$的签名的色数是顶点$ | v（h）的最小数量，签名的图形$（h，π）$的$（g，σ）$允许同型同构。签名图的Homorphisms在过去的几十几十数学上都吸引了增长的注意力，尤其是它们的图形颜色，尤其是图形的图形，并且图形的图形是及其图形的绘制。通过签名色数的范围，对这些同态进行了特别研究。在这项工作中，我们在几个签名图的家族（平面图，无三角形平面图，$ k_n $ -minor -minor-minor-fre-minor图形和界限图）的几个家族中提供了新的结果和界限。
A signed graph $(G, σ)$ is a graph $G$ along with a function $σ: E(G) \to \{+,-\}$. A closed walk of a signed graph is positive (resp., negative) if it has an even (resp., odd) number of negative edges, counting repetitions. A homomorphism of a (simple) signed graph to another signed graph is a vertex-mapping that preserves adjacencies and signs of closed walks. The signed chromatic number of a signed graph $(G, σ)$ is the minimum number of vertices $|V(H)|$ of a signed graph $(H, π)$ to which $(G, σ)$ admits a homomorphism.Homomorphisms of signed graphs have been attracting growing attention in the last decades, especially due to their strong connections to the theories of graph coloring and graph minors. These homomorphisms have been particularly studied through the scope of the signed chromatic number. In this work, we provide new results and bounds on the signed chromatic number of several families of signed graphs (planar graphs, triangle-free planar graphs, $K_n$-minor-free graphs, and bounded-degree graphs).
