关键词: Bipartite graph, random graph, minimum congestion spanning tree

Abstract:

The first problem considered in this article reads: is it possible to find upper estimates for the spanning tree congestion in bipartite graphs, which are better than those for general graphs? It is proved that there exists a bipartite version of the known graph with spanning tree congestion of order n^3/2, where n is the number of vertices. The second problem is to estimate spanning tree congestion of random graphs. It is proved that the standard model of random graphs cannot be used to find graphs whose spanning tree congestion has order
greater than n^3/2.

Key words: Bipartite graph, random graph, minimum congestion spanning tree