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Lee-Yang Phenomena in Edge-Coloured Graph Counting

Authors: Maximilian Wiesmann

Published in: LIPIcs, Volume 381, 37th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2026)


Abstract
We describe the accumulation of complex zeros of a univariate polynomial arising from the enumeration of edge-coloured graphs along certain limit curves. The polynomial is a variant of an edge-chromatic polynomial, which specialises to the partition function of the ferromagnetic Ising model on a random regular graph. We call this accumulation behaviour a Lee-Yang phenomenon in analogy with the Lee-Yang theorem from statistical physics. The limiting loci are semialgebraic and arise from anti-Stokes curves of an exponential integral.

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Maximilian Wiesmann. Lee-Yang Phenomena in Edge-Coloured Graph Counting. In 37th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 381, pp. 31:1-31:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)


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@InProceedings{wiesmann:LIPIcs.AofA.2026.31,
  author =	{Wiesmann, Maximilian},
  title =	{{Lee-Yang Phenomena in Edge-Coloured Graph Counting}},
  booktitle =	{37th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2026)},
  pages =	{31:1--31:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-435-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{381},
  editor =	{Panagiotou, Konstantinos},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2026.31},
  URN =		{urn:nbn:de:0030-drops-263028},
  doi =		{10.4230/LIPIcs.AofA.2026.31},
  annote =	{Keywords: Chromatic Polynomial, edge-coloured Graph, asymptotic Enumeration, exponential Integral, Lee-Yang Zeros, Ising Model, Partition Function}
}
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