The existence of biregular spanning subgraphs in bipartite graphs via spectral radius

Abstract: Biregular bipartite graphs have been proven to have similar edge distributions to random bipartite graphs and thus have nice pseudorandomness and expansion properties. Thus it is quite desirable to find a biregular bipartite spanning subgraph in a given bipartite graph. In fact, a theorem of Ore implies a structural characterization of such subgraphs in bipartite graphs. In this paper, we demonstrate the existence of biregular bipartite spanning subgraphs in bipartite graphs by employing spectral radius. We also study the existence of spanning trees with restricted degrees and edge-disjoint spanning trees in bipartite graphs via spectral radius.