Polynomial Gyárfás–Sumner conjecture for graphs of bounded boxicity

James C. Davies; Yelena Yuditsky

doi:10.5802/igt.17

April 2, 2026Innovations in Graph Theory

Polynomial Gyárfás–Sumner conjecture for graphs of bounded boxicity

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Key Points

The study aims to prove the polynomial χ-boundedness of intersection graphs of axis-aligned boxes with no induced subgraph from a specified forest.
Proved the polynomial χ-bounded property for intersection graphs of axis-aligned boxes in Euclidean space.
Analyzed the implications of bounding boxicity in graph structures.
Utilized properties of forests to establish results about induced subgraphs.
Confirmed that intersection graphs are polynomially χ-bounded under specified conditions.
Established a relationship between boxicity and the structure of the involved forests.
Provided a framework for understanding graph properties in high dimensional spaces.

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Implication

This research demonstrates χ-boundedness in graphs of bounded boxicity, implying new insights into graph theory.

Abstract

We prove that for every positive integer d and forest F , the class of intersection graphs of axis-aligned boxes in ℝ d with no induced F subgraph is (polynomially) χ -bounded.

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Cite This Study

Davies et al. (2026) studied this question.

synapsesocial.com/papers/69cf5ede5a333a821460d8e0 https://doi.org/10.5802/igt.17

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Polynomial Gyárfás–Sumner conjecture for graphs of bounded boxicity

Key Points

Ask about this paper

Implication

Abstract

Discussion

Cite This Study

Polynomial Gyárfás–Sumner conjecture for graphs of bounded boxicity

Key Points

Ask about this paper

Implication

Abstract

Discussion

Cite This Study

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