Even factors with a bounded number of components in iterated line graphs

We consider even factors with a bounded number of components in the n-times iterated line graphs L ⁿ (G). We present a characterization of a simple graph G such that L ⁿ (G) has an even factor with at most k components, based on the existence of a certain type of subgraphs in G. Moreover, we use this result to give some upper bounds for the minimum number of components of even factors in L ⁿ (G) and also show that the minimum number of components of even factors in L ⁿ (G) is stable under the closure operation on a claw-free graph G, which extends some known results. Our results show that it seems to be NP-hard to determine the minimum number of components of even factors of iterated line graphs. We also propose some problems for further research.