Burr's Conjecture on Oriented Trees in Digraphs

Core Concepts

Providing subquadratic bounds for Burr's conjecture on oriented trees in digraphs.

Abstract

The article discusses Burr's conjecture on oriented trees in digraphs, providing subquadratic bounds. It explores necessary conditions for graphs to contain specific subgraphs based on chromatic numbers. The paper introduces a win-win strategy for deriving universality bounds for trees by induction, gluing leaves or paths depending on the number of leaves. Various theorems and lemmas are presented to support the main argument.

Stats

Burr's conjecture states that every oriented tree of order k is (2k - 2)-universal. The paper provides subquadratic bounds for oriented trees in digraphs.

Quotes

"In essence, many of the questions in structural graph theory ask for necessary conditions for a (di)graph to contain some other given (di)graph." "Every oriented tree of order k is (k^2/2 - k^2 + 1)-universal."

Key Insights Distilled From

Oriented trees in $O(k \sqrt{k})$-chromatic digraphs, a subquadratic bound for Burr's conjecture

by Stép... at arxiv.org 03-01-2024

https://arxiv.org/pdf/2402.19351.pdf

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