On Maximum Weight of a Bipartite Graph of Given Order and Size
Discussiones Mathematicae Graph Theory, Tome 33 (2013) no. 1, p. 147.

Voir la notice de l'article dans European Digital Mathematics Library

The 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 Erd˝os 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.
Classification : 05C22, 05C35
Mots-clés : weight of an edge, weight of a graph, bipartite graph., bipartite graph 
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Mirko Horňák; Stanislav Jendrol’; Ingo Schiermeyer. On Maximum Weight of a Bipartite Graph of Given Order and Size. Discussiones Mathematicae Graph Theory, Tome 33 (2013) no. 1, p. 147. https://geodesic-test.mathdoc.fr/item/DMGT_2013__33_1_267989/