Bruce Reed

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20242026

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math.CO2024

Embedding Nearly Spanning Trees

Bruce Reed, Maya Stein

The Erdős-Sós Conjecture states that every graph with average degree exceeding $k - 1$ contains every tree with $k$ edges as a subgraph. We prove that there are $δ > 0$ and $k_0\in\mat…

math.CO2024

Vertex Ranking of Degenerate Graphs

John Iacono, Piotr Micek, Pat Morin +1

An $ℓ$ -vertex-ranking of a graph $G$ is a colouring of the vertices of $G$ with integer colours so that in any connected subgraph $H$ of $G$ with diameter at most $ℓ$ , there…

math.CO2024

Linear bounds on treewidth in terms of excluded planar minors

J. Pascal Gollin, Kevin Hendrey, Sang-il Oum +1

One of the fundamental results in graph minor theory is that for every planar graph $H$ , there is a minimum integer $f (H)$ such that graphs with no minor isomorphic to $H$ have tre…