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：若存在一棵边带权（权值为非负实数）的树T以及非负实数半轴上的不相交区间，使得图G的每个节点唯一对应T的一个叶子节点，并且当且仅当两个叶子节点在T中的加权距离位于任一此类区间内时，它们在G中对应的节点之间存在边，则称图G为多区间PCG。若区间数量为k，则称该图为k区间PCG；记作G = k区间-PCG (T, I1, ..., Ik)。已知2区间-PCG不能包含所有图，目前已知不属于此类的最小图具有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，从而为确定“存在不属于2区间-PCG的n节点图”的最小n值迈出了一步。