Abstract
AbstractIn this paper are investigated maximum bipartite subgraphs of graphs, i.e., bipartite subgraphs with a maximum number of edges. Such subgraphs are characterized and a criterion is given for a subgraph to be a unique maximum bipartite subgraph of a given graph. In particular maximum bipartite subgraphs of cubic graphs are investigated. It is shown that cubic graphs can be built up from five building stones (called elementary paths). Finally the investigation of a special class of cubic graphs yields a theorem which characterizes the Petersen graph and the dodecahedron graph by means of their maximum bipartite subgraphs.
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