Forbidden pairs for connected even factors in supereulerian graphs (Q6115432)

A graph is supereulerian if it has a spanning Eulerian subgraph. A connected even [2, 2\(s\)]-factor of a graph \(G\) is a connected factor with all vertices of even degree. The authors establish necessary and sufficient conditions for every connected supereulerian \(H\)-free graph \(G\) that it contains a connected even \([2, 2k]\)-factor, for a positive integer \(k\le 4\).