Bruce Reed

collaborators

3 papers

math.CO2025

Embedding Nearly Spanning Trees

Bruce Reed, Maya Stein

The ErdÅs-SÃ³s 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 $I^´ > 0$ and $k_0\in\…

math.CO2025

The asymptotic $I ¨ $ -boundedness of hereditary families

Bruce Reed, Yelena Yuditsky

A family $F$ of graphs is asymptotically $I ¨ $ -bounded with bounding function $f$ if almost every graph $G$ in the family satisfies $I ¨ (G) \leq f (I ¨ (G))$ . A graph is $H$ -free…

math.CO2025

Typical $T$ -free graphs

Bruce Reed, Yelena Yuditsky

We prove that for every tree $T$ which is not an edge, for almost every graph $G$ which does not contain $T$ as an induced subgraph, $V (G)$ has a partition into $I^\pm (T) - 1$ parts cer…

Embedding Nearly Spanning Trees

The asymptotic I¨-boundedness of hereditary families

Typical T-free graphs

The asymptotic $I ¨ $ -boundedness of hereditary families

Typical $T$ -free graphs