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Counterexamples to Clique Immersion Conjecture for Direct Products
Chuanshu Wu, Zijian Deng
Let \(G\) and \(H\) be graphs, and let \(G\times H\) denote their direct product. For a graph \(G\), let \(\operatorname{im}(G)\) be the largest integer \(t\) such that \(G\) conta…
Odd complete bipartite minors in graphs with independence number two
Rong Chen, Zijian Deng
Recently, Chen and Deng have proved that every graph with independence number two contains as a minor for each integer with . In…
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 contains an immersion of the complete graph . Vergara showed that this is equivalent to sayin…
Connected matching in graphs with independence number two
Rong Chen, Zijian Deng
A matching in a graph is {\em connected} if has an edge linking each pair of edges in . The problem to find large connected matchings in graphs with is…
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 contains every complete bipartite graph on vertices as a minor, where is the ch…