Bruce Reed

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2 papers · 1 filter

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.CO2014

A Density Version of the Corradi-Hajnal Theorem

Dieter Rautenbach, Bruce Reed

For every positive integer $k$ , we show that every graph of order $n$ at least $3 k$ with more than $max {(2 2 k - 1) + (2 k - 1) (n - (2 k - 1)), (2 3 k - 1) + (n - (3 k - 1))}$ edges has…