Given a set system $\mathcal{X} = \{\mathcal{U},\mathcal{S}\}$, where $\mathcal{U}$ is a set of elements and $\mathcal{S}$ is a set of subsets of $\mathcal{U}$, an exact hitting set $\mathcal{U}'$ is a subset of $\mathcal{U}$ such that each subset in $\mathcal{S}$ contains exactly one element in $\mathcal{U}'$. We refer to a set system as exactly hittable if it has an exact hitting set. In this paper, we study interval graphs which have intersection models that are exactly hittable. We refer to these interval graphs as exactly hittable interval graphs (EHIG). We present a forbidden structure characterization for EHIG. We also show that the class of proper interval graphs is a strict subclass of EHIG. Finally, we give an algorithm that runs in polynomial time to recognize graphs belonging to the class of EHIG.
翻译：根据一个设定的系统 $\ mathcal{X} = mathcal{X} = mathcal{U} {U},\ mathcal{S} {S} $\ mathcal{U} = mathcal{S} = mathcal{U}, $\ mathcal{S} = mathcal{S} $ = 设置的系统是一组元素, 而$\ mathcal{S} {U} $ 是一组元素的集合, 而$\ mathcal{U} = 美元是一组元素, 而$\ mathcal{U} = 美元是一组子集的子集, 美元是一组元素是一组元素 $\ mathcal{ {U} 。 我们在此文件中将一个设置的设置的系统称为完全可以击中的精确击中的系统。 在本文中, 我们研究具有交叉模型的间图是完全可以击中的间隔图。 我们将这些图称为精确的间隔图称为 sheckable 。 我们将这些图称为 EIG 类的。 。 我们把这些图称为精确的 。 。 。 我们用 。 我们把这些图解算算算算出属于EHIG 。
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