Each hereditary property can be characterized by its set of minimal obstructions; these sets are often unknown, or known but infinite. By allowing extra structure it is sometimes possible to describe such properties by a finite set of forbidden objects. This has been studied most intensely when the extra structure is a linear ordering of the vertex set. For instance, it is known that a graph G is $k$-colourable if and only if $V\left(G\right)$ admits a linear ordering $\le$ with no vertices $v_1\le \cdots \le v_{k+1}$ such that $v_i{v}_{i+1}\in E\left(G\right)$ for every $i\in \{1,\cdots ,k\}$. In this paper, we study such characterizations when the extra structure is a circular ordering of the vertex set. We show that the classes that can be described by finitely many forbidden circularly ordered graphs include forests, circular-arc graphs, and graphs with circular chromatic number less than $k$. In fact, every description by finitely many forbidden circularly ordered graphs can be translated to a description by finitely many forbidden linearly ordered graphs. Nevertheless, our observations underscore the fact that in many cases the circular order descriptions are nicer and more natural.

每个遗传属性都可以通过其最小障碍集来表征；这些集合通常是未知的，或已知但无限的。通过允许额外的结构，有时可以通过一组有限的禁止对象来描述这些属性。当额外的结构是顶点集的线性排序时，这已经得到了最深入的研究。例如，已知图 G 是$ķ$- 可着色当且仅当$五\left(G\right)$承认线性排序$\le$没有顶点$v_1\le \cdots \le v_{ķ+1}$这样$v_{\mathrm{一世}}{v}_{\mathrm{一世}+1}\in 乙\left(G\right)$对于每个$\mathrm{一世}\in \{1,\cdots ,ķ\}$. 在本文中，我们研究了当额外结构是顶点集的循环排序时的这种表征。我们证明了可以用有限多个禁止循环有序图描述的类包括森林、圆弧图和圆色数小于$ķ$. 事实上，有限多禁止循环有序图的每个描述都可以转换为有限多禁止线性有序图的描述。尽管如此，我们的观察强调了这样一个事实，即在许多情况下，循环顺序描述更好、更自然。