Strong cocomparability graphs are the reflexive graphs whose adjacency matrix can be rearranged by a simultaneous row and column permutation to avoid the submatrix with rows $01, 10$. Strong cocomparability graphs form a subclass of cocomparability graphs (i.e., the complements of comparability graphs) and can be recognized in polynomial time. In his seminal paper, Gallai characterized cocomparability graphs in terms of a forbidden structure called asteroids. Gallai proved that cocomparability graphs are precisely those reflexive graphs which do not contain asteroids. In this paper, we give a characterization of strong cocomparability graphs which is analogous to Gallai's characterization for cocomparability graphs. We prove that strong cocomparability graphs are precisely those reflexive graphs which do not contain weak edge-asteroids (a weaker version of asteroids). Our characterization also leads to a polynomial time recognition algorithm for strong cocomparability graphs.

翻译：强共可比性图是自反图，其邻接矩阵可通过同时的行列置换避免出现子矩阵行$01, 10$。强共可比性图构成共可比性图（即可比性图的补图）的一个子类，且可在多项式时间内识别。在其开创性论文中，Gallai利用称为星形体的禁止结构刻画了共可比性图。Gallai证明了共可比性图恰为不含星形体的自反图。本文给出了强共可比性图的一种刻画，该刻画类似于Gallai对共可比性图的刻画。我们证明了强共可比性图恰为不含弱边星形体（星形体的弱化版本）的自反图。该刻画还导出了强共可比性图的多项式时间识别算法。