Asymptotic normality of embedding distributions of some families of graphs

2025/07/21 by Chen, Yichao, Fang, Wenjie, Gao, Zhicheng +1
#05A15 #05A16 #05C10 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.15751

Abstract

Computing the embedding distribution of a given graph is a fundamental question in topological graph theory. In this article, we extend our viewpoint to a sequence of graphs and consider their asymptotic embedding distributions, which are often the normal distribution. We establish the asymptotic normality of several families of graphs by developing adapted tools and frameworks. We expect that these tools and frameworks can be used on other families of graphs to establish the asymptotic normality of their embedding distributions. Several open questions and conjectures are also raised in our investigation.

Citations

• Strong log-convexity of genus sequences
• Genus Polynomials of Cubic Graphs with Non-Real Roots
• Limits for embedding distributions
• Geometry of limits of zeros of polynomial sequences of type (1,2)
• On the combinatorial local log-concavity conjecture and a result of Stanley
• Root geometry of polynomial sequences II: Type (1,0)
• Iterated claws have real-rooted genus polynomials
• Root geometry of polynomial sequences I: Type (0,1)
• Two Enumerative Results on Cycles of Permutations

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