标题： 三角重图的度序列 显示英文标题

标题： Degree sequences of triangular multigraphs

摘要： 一个简单图被称为三角形图，如果每条边都包含在一个三角形中。 一个整数序列被称为图序列，如果它是某个简单图的度序列。 Egan 和 Nikolayevsky 最近猜想，每个项都至少为 4 的图序列都是某个三角形简单图的度序列，并且在一些特殊情况下证明了这一点。 本文中我们陈述并证明了这个猜想对于多重图的类比版本。 显示英文摘要

摘要： A simple graph is triangular if every edge is contained in a triangle. A sequence of integers is graphical if it is the degree sequence of a simple graph. Egan and Nikolayevsky recently conjectured that every graphical sequence whose terms are all at least 4 is the degree sequence of a triangular simple graph, and proved this in some special cases. In this paper we state and prove the analogous version of this conjecture for multigraphs.