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

TL;DR

This paper investigates the existence of biregular spanning subgraphs and certain spanning trees in bipartite graphs using spectral radius techniques, revealing new structural insights and conditions.

Contribution

It introduces spectral radius methods to establish the existence of biregular spanning subgraphs and degree-restricted spanning trees in bipartite graphs, extending prior structural results.

Findings

Existence of biregular spanning subgraphs proven via spectral radius.

Conditions for spanning trees with restricted degrees established.

Results enhance understanding of bipartite graph structures.

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.