Tiling tripartite graphs with 3-colorable graphs

Tiling tripartite graphs with 3-colorable graphs: The extreme case

There is a sufficiently large $N\in h\mathbb{N}$ such that the following holds. If $G$ is a tripartite graph with $N$ vertices in each vertex class such that every vertex is adjacent to at least $2N/3+2h-1$ vertices in each of the other classes, then $G$ can be tiled perfectly by copies of $K_{h,h,h}$. This extends work by two of the authors [Electron. J. Combin, 16(1), 2009] and also gives a sufficient condition for tiling by any fixed 3-colorable graph. Furthermore, we show that $2N/3+2h-1$ in our result can not be replaced by $2N/3+ h-2$ and that if $N$ is divisible by $6h$, then we can rep…

一种证明四色定理的更新方法（无需计算机）第二部分：极值非四色可染极大平面图中的 R/G/B Kempe 链

A renewal approach to prove the Four Color Theorem unplugged, Part II: R/G/B Kempe chains in an extremum non-4-colorable MPG

本文通过 R/G/B Kempe 链和 RGB 铺砌重新审视极值非四色可染极大平面图，提出无需计算机验证四色定理的更新方法，并发现一系列与四色可染性相关的基本定理。

固定偶数大小的局部反幻3-可着色图的构造——矩阵方法

Construction of local antimagic 3-colorable graphs of fixed even size -- matrix approach

本文研究了局部反幻着色图的构造问题，提出了一种基于整数矩阵的构造方法，成功获得了许多大小为$10k$且局部反幻色数为3的（不连通）二部和三部图族。

一种无需计算机证明四色定理的革新方法，第一部分：极大平面图上的 RGB-铺砌

A renewal approach to prove the Four Color Theorem unplugged, Part I: RGB-tilings on maximal planar graphs

本文提出不用计算机检验证明四色定理的三部分新方案，首篇在极大平面图上建立R/G/B与RGB边铺砌及其与顶点4-着色的联系。

关于三部图及其以外的色谱

On the chromatic profile for tripartite graphs and beyond

本文研究了三部图及其扩展的色谱问题，证明了当r=2且H的色数为3时，δ_χ(H,2)的可能值集是有限且离散的，并给出了每个阈值对应的图结构特征。