带度约束的图

Workshop on Analytic Algorithmics and Combinatorics Pub Date : 2015-06-09 DOI:10.1137/1.9781611974324.4

Élie de Panafieu, Lander Ramos

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引用次数: 10

摘要

给定一个非负整数集D，我们导出了图的渐近数目，这些图具有给定数目的顶点和边，并且每个顶点的度数都在D内。这推广了已有的结果，例如具有给定最小度数的图的枚举，并建立了新的结果，例如所有顶点都具有偶数度数的欧拉图的枚举。这些结果是用解析组合学推导出来的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Graphs with degree constraints

Given a set D of nonnegative integers, we derive the asymptotic number of graphs with a givenvnumber of vertices, edges, and such that the degree of every vertex is in D. This generalizes existing results, such as the enumeration of graphs with a given minimum degree, and establishes new ones, such as the enumeration of Euler graphs, i.e. where all vertices have an even degree. Those results are derived using analytic combinatorics.

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Workshop on Analytic Algorithmics and Combinatorics

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