The computational complexity of the graph isomorphism problem is considered to be a major open problem in theoretical computer science. It is known that testing isomorphism of chordal graphs is polynomial-time equivalent to the general graph isomorphism problem. Every chordal graph can be represented as the intersection graph of some subtrees of a representing tree, and the leafage of a chordal graph is defined to be the minimum number of leaves in a representing tree for it. We prove that chordal graph isomorphism is fixed parameter tractable with leafage as parameter. In the process we introduce the problem of isomorphism testing for higher-order hypergraphs and show that finding the automorphism group of order-$k$ hypergraphs with vertex color classes of size $b$ is fixed parameter tractable for any constant $k$ and $b$ as fixed parameter.

翻译：图形的计算复杂度被认为是理论计算机科学中一个主要的开放问题。 众所周知, 相形图的测试是多数值- 时间, 相当于一般图形的异形问题。 每个相形图可以作为代表树的一些亚树的交叉图, 色体图的叶子被定义为代表树的树叶的最低数量。 我们证明, 相形图的形态是固定参数, 参数可以与叶叶作为参数一起绘制。 在此过程中, 我们引入了高阶高调图的异形测试问题, 并表明, 找到具有顶端颜色等级的奥序- $k$ 的超大图是固定参数, 任何常值 $ 和 $ $b 的固定参数都是固定的 。