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

R Chen, Z Deng - arXiv preprint arXiv:2412.04522, 2024 - arxiv.org
Hadwiger's conjecture for the immersion relation posits that every graph $ G $ contains an
immersion of the complete graph $ K_ {\chi (G)} $. Vergara showed that this is equivalent to …

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

R Chen, Z Deng - arXiv preprint arXiv:2406.02643, 2024 - arxiv.org
Woodall (and Seymour independently) in 2001 proposed a conjecture that every graph $ G
$ contains every complete bipartite graph on $\chi (G) $ vertices as a minor, where $\chi (G) …