Geodesic
Forbidden Subgraphs for Collapsible Graphs and Supereulerian Graphs
Discussiones Mathematicae. Graph Theory, Tome 42 (2022) no. 2, pp. 417-442

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In this paper, we completely characterize the connected forbidden subgraphs and pairs of connected forbidden subgraphs that force a 2-edge-connected (2-connected) graph to be collapsible. In addition, the characterization of pairs of connected forbidden subgraphs that imply a 2-edge-connected graph of minimum degree at least three is supereulerian will be considered. We have given all possible forbidden pairs. In particular, we prove that every 2-edge-connected noncollapsible (or nonsupereulerian) graph of minimum degree at least three is Z3-free if and only if it is K3-free, where Zi is a graph obtained by identifying a vertex of a K3 with an end-vertex of a Pi+1.
Keywords: forbidden subgraph, supereulerian, collapsible 
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Liu, Xia; Xiong, Liming. Forbidden Subgraphs for Collapsible Graphs and Supereulerian Graphs. Discussiones Mathematicae. Graph Theory, Tome 42 (2022) no. 2, pp. 417-442. http://geodesic.mathdoc.fr/item/DMGT_2022_42_2_a6/