Non-repetitive 3-coloring of subdivided graphs.

Pezarski, Andrzej; Zmarz, Michał

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Notes on nonrepetitive graph colouring.

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On Maximum Weight of a Bipartite Graph of Given Order and Size

Mirko Horňák, Stanislav Jendrol’, Ingo Schiermeyer (2013)

Discussiones Mathematicae Graph Theory

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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...