「色彩約束生成樹問題」或「出度色彩約束生成樹問題」旨在邊著色圖上找到一個生成樹，使得和每一個節點相鄰的邊（或出邊）中，顏色相同的邊數少於一個給定的常數。我們探討此問題中存在多項式時間複雜度演算法的特例。其中，當給定邊著色圖為有向無環圖時，出度色彩約束生成樹問題可由網路最大流或是擬陣相關算法解開。除此之外，參數為１的色彩約束生成樹問題在只有兩種顏色的邊著色圖上可以透過動態規劃在線性時間內解開。

The κ-Colored Constrained Spanning Tree (κ-CCST) and the κ-Colored Out-Constrained Spanning Tree (κ-COCST) problems on edge-colored directed graphs target to find a spanning tree such that for each vertex, the number of incident edges (or, outgoing edges) that share any specific color is bounded by some constant κ. We discussed special cases where polynomial-time algorithms exist. In particular, when the input graph is a directed acyclic graph (DAG), the κ-COCST problem can be solved via a maximum-flow-based algorithm or a matroid-based algorithm. Furthermore, the 1-CCST problem can be solved via dynamic programming in linear time in 2-edge-colored graphs.

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