Title: On clique immersions in line graphs

 

 

Abstract: Many problems exist at the intersection of structural and chromatic graph theory. One of the longest standing open problems in this domain is a conjecture of Hadwiger which posits that all graphs with chromatic number at least t contain a clique on t vertices as a minor. Abu-Khzam and Langston have conjectured an analogous result where an immersion of a clique on t vertices is the necessary substructure. In this talk, I will discuss the status of these conjectures for line graphs. I will also establish an equivalence between these two relations in line graphs in the case of cliques of size at most 4.