Biclique immersions in graphs with independence number 2

03/11/2023

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by   F. Botler, et al.

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The analog of Hadwiger's conjecture for the immersion relation states that every graph G contains an immersion of K_χ(G). For graphs with independence number 2, this is equivalent to stating that every such n-vertex graph contains an immersion of K_⌈ n/2 ⌉. We show that every n-vertex graph with independence number 2 contains every complete bipartite graph on ⌈ n/2 ⌉ vertices as an immersion.