A vertebrate interval graph is an interval graph in which the maximum size of a set of independent vertices equals the number of maximal cliques. For any fixed $v \ge 1$, there is a polynomial-time algorithm for deciding whether a vertebrate interval graph admits a vertex partition into two induced subgraphs with claw number at most $v$. In particular, when $v = 2$, whether a vertebrate interval graph can be partitioned into two proper interval graphs can be decided in polynomial time.

翻译：脊椎间距图是一个间距图,其中一组独立的脊椎的最大大小等于最大圆柱形的数目。对于任何固定的 $v\ge 1$,有一个多元时间算法来决定一个脊椎间距图是否将一个脊椎间距分区纳入两个引导子图,其爪号最多为$v = 2美元。特别是当 $v = 2美元时,一个脊椎间距图能否被分割成两个适当的间距图,可以在多元时间中决定。