We study the question of whether a sequence d = (d_1,d_2, \ldots, d_n) of positive integers is the degree sequence of some outerplanar (a.k.a. 1-page book embeddable) graph G. If so, G is an outerplanar realization of d and d is an outerplanaric sequence. The case where \sum d \leq 2n - 2 is easy, as d has a realization by a forest (which is trivially an outerplanar graph). In this paper, we consider the family \cD of all sequences d of even sum 2n\leq \sum d \le 4n-6-2\multipl_1, where \multipl_x is the number of x's in d. (The second inequality is a necessary condition for a sequence d with \sum d\geq 2n to be outerplanaric.) We partition \cD into two disjoint subfamilies, \cD=\cD_{NOP}\cup\cD_{2PBE}, such that every sequence in \cD_{NOP} is provably non-outerplanaric, and every sequence in \cD_{2PBE} is given a realizing graph $G$ enjoying a 2-page book embedding (and moreover, one of the pages is also bipartite).

翻译：我们研究正整数序列 d = (d₁,d₂,…,dₙ) 是否为某个外平面图（即1页书可嵌入图）的度序列的问题。若是，则称 G 为 d 的外平面实现，d 为外平面序列。当 Σd ≤ 2n−2 时情形简单，因 d 可由森林实现（森林显然为外平面图）。本文考虑所有偶和序列 d 构成的族 𝒟，满足 2n ≤ Σd ≤ 4n−6−2μ₁，其中 μₓ 表示 d 中 x 的个数。（第二不等式是 Σd≥2n 的序列 d 为外平面的必要条件。）我们将 𝒟 划分为两个互斥子族 𝒟 = 𝒟_{NOP} ∪ 𝒟_{2PBE}，使得 𝒟_{NOP} 中每个序列可证为非外平面序列，而 𝒟_{2PBE} 中每个序列均给出一个实现图 G，该图具有2页书嵌入（且其中一页为二分图）。