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EXPOSITIO

A home for expository scholarship

Expositio is a repository for expository papers in a wide range of academic disciplines, supporting preprints, revisions, optional peer review, saved papers, and overlay journals.

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What is Expositio?

A public repository for expository academic papers, with an integrated scholarly record.

Expositio is a place to read and cite expository work. Papers are published as stable, citable records, while remaining connected to later versions, editorial decisions, and related context.

Some papers are early drafts; others have been peer reviewed or formally published. Each paper remains readable on its own, while preserving the history behind it.

The result is both a reading room and a record: a place to browse by field, read papers in stable form, and follow their development over time.

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Graph theory

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Mathematics › Combinatorics › Graph theory
Domain: Mathematics × Branch: Combinatorics × Branch: Graph theory ×

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Preprint
v1

Sidorenko's conjecture predicts that the homomorphism density of a bipartite graph H in a host graph G satisfies t_H(G) ≥ t_{K_2}(G)^|E(H)|. We introduce the conjecture through homomorphism densities, prove the finite-host inequality for P_3, C_4, and the complete bipartite grap…

Mathematics / Combinatorics
Mathematics > Combinatorics > Density (toughness, etc.) Primary
Public since Aug 7, 2026 1 save
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Expositio paper

How Close Can a Chromatic Root Get to One?

Arnav Dhiman

Preprint
v1

In this paper we show that the chromatic function $P(G,t)$ is always a polynomial. We then ask a simple question: where does this polynomial equal zero? Tutte showed that two stretches of the real line, $(-\infty,0)$ and $(0,1)$, can never contain a root. Jackson showed in 1993 …

Mathematics / Combinatorics
Mathematics > Combinatorics > Coloring of graphs and hypergraphs Primary
Public since Aug 7, 2026 0 saves
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