Supereulerianity of image-edge-connected graphs with a restriction on small bonds Original Research Article

Let image be integers, and let image denote the graph family such that a graph image of order image is in image if and only if image is image-edge-connected such that for every bond image with image, each component of image has order at least image. In this paper, we show that if image with image, then either image is supereulerian or it is contractible to the Petersen graph. A graph is image-supereulerian if it has a spanning even subgraph with at most image components. We also prove the following: if image with image and image, then image is image-supereulerian; if image with image, then image is image-supereulerian; if image with image and image, then image is image-supereulerian.