Counting the number of linear extensions of a partial order was considered by Stanley about 50 years ago. For the partial order on the vertices and edges of a graph determined by inclusion, we call such linear extensions {\it construction sequences} for the graph as each edge follows both of its endpoints. The number of such sequences for paths, cycles, stars, double-stars, and complete graphs is found. For paths, we agree with Stanley (the Tangent numbers) and get formulas for the other classes. Structure and applications are also studied.

翻译：关于偏序集线性扩展的计数问题，斯坦利在约50年前已有研究。对于由包含关系确定的图中顶点与边构成的偏序集，我们称其线性扩展为图的"构造序列"，因为每条边均在其两个端点之后出现。我们求出了路径图、圈图、星图、双星图及完全图这类序列的数目。对于路径图，我们的结果与斯坦利（正切数）一致，并给出了其他图类的公式。此外，我们还研究了其结构与应用。