Dedicated to Mietek Borowiecki on the occasion of his seventieth birthday.
On maximum weight of a bipartite graph
of given order and size
Institute of Mathematics
|Ingo Schiermeyer |
Institut für Diskrete Mathematik und Algebra
AbstractThe weight of an edge xy of a graph is defined to be the sum of degrees of the vertices x and y. The weight of a graph G is the minimum of weights of edges of G. More than twenty years ago Erdos was interested in finding the maximum weight of a graph with n vertices and m edges. This paper presents a complete solution of a modification of the above problem in which a graph is required to be bipartite. It is shown that there is a function w*(n,m) such that the optimum weight is either w*(n,m) or w*(n,m)+1.
Keywords: weight of an edge, weight of a graph, bipartite graph
2010 Mathematics Subject Classification: 05C35.
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Received 2 February 2012
Revised 8 January 2012
Accepted 9 January 2012