本論文提出兩個自我穩定（Self-stabilizing）的圖形之無環路塗色（Acyclic Colorings of Graph）演算法，解決分散式系統中的無環路塗色問題。第一個演算法用在有向無環路圖形（Directed Acyclic Graph）上，第二個演算法則用在無K4子圖的圖形（K4-free Graph）上。
第一個演算法用在一般的圖形（General Graph）上時，它最多需要使用1+D/2種顏色；在完全二裂圖形（Complete Bipartite Graph）上，它只需使用2種顏色；而在平面圖形（Planar Graph）上，它只需使用3種顏色。第二個演算法則用在無K4子圖的圖形（K4-free Graph）上，圖形中需有一個特殊點（special node），其他個點均互不可分辨（nuiform），此演算法只需使用2種顏色。

This thesis proposes two self-stabilizing algorithms for acyclic colorings of graphs. An acyclic coloring of a graph G is a coloring of the vertices of G such that the vertices with the same color in G induces an acyclic subgraph. The first algorithm we proposed needs 2 colors for a complete bipartite graph, or less than 1+D/2 colors for a general graph, where D is the degree of G. Both graphs must be acyclic oriented in advance. In some special acyclic orientation, it needs only 3 colors for a planar graph, or a K3,3-free or K5-free graph. The second algorithm we proposed is for a K4-free and rooted graph, and it needs only 2 colors.

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