A graph G is a multi-interval PCG if there exist an edge weighted tree T with non-negative real values and disjoint intervals of the non-negative real half-line such that each node of G is uniquely associated to a leaf of T and there is an edge between two nodes in G if and only if the weighted distance between their corresponding leaves in T lies within any such intervals. If the number of intervals is k, then we call the graph a k-interval-PCG; in symbols, G = k-interval-PCG (T, I1, . . . , Ik). It is known that 2-interval-PCGs do not contain all graphs and the smallest known graph outside this class has 135 nodes. Here we prove that all graphs with at most 8 nodes are 2-interval-PCGs, so doing one step towards the determination of the smallest value of n such that there exists an n node graph that is not a 2-interval-PCG.

翻译：图G称为多区间PCG，若存在一棵边赋权树T（边权为非负实数）以及非负实数半轴上的若干互不相交的区间，使得G中每个节点唯一对应于T的一片叶子，且G中两节点之间存在边当且仅当它们对应叶子之间的加权距离落于上述某个区间内。若区间个数为k，则称该图为k-区间-PCG，记为G = k-区间-PCG (T, I1, . . . , Ik)。已知2-区间-PCG类并不包含所有图，且目前已知不属于该类的最小图包含135个节点。本文证明所有节点数不超过8的图均为2-区间-PCG，从而向确定非2-区间-PCG图的最小节点数n迈进一步。