Rong Chen

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4 papers · 1 filter

math.CO2025

Odd complete bipartite minors in graphs with independence number two

Rong Chen, Zijian Deng

Recently, Chen and Deng have proved that every graph $G$ with independence number two contains $K_{ℓ, χ (G) - ℓ}$ as a minor for each integer $ℓ$ with $1 \leq ℓ < χ (G)$ . In…

math.CO2024

A simple proof of the existence of complete bipartite graph immersion in graphs with independence number two

Rong Chen, Zijian Deng

Hadwiger's conjecture for the immersion relation posits that every graph $G$ contains an immersion of the complete graph $K_{χ (G)}$ . Vergara showed that this is equivalent to sayin…

math.CO2024

Connected matching in graphs with independence number two

Rong Chen, Zijian Deng

A matching $M$ in a graph $G$ is {\em connected} if $G$ has an edge linking each pair of edges in $M$ . The problem to find large connected matchings in graphs $G$ with $α (G) = 2$ is…

math.CO2024

Seymour and Woodall's conjecture holds for graphs with independence number two

Rong Chen, Zijian Deng

Woodall (and Seymour independently) in 2001 proposed a conjecture that every graph $G$ contains every complete bipartite graph on $χ (G)$ vertices as a minor, where $χ (G)$ is the ch…