Gábor Lippner

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The classical theorem of Vizing states that every graph of maximum degree d admits an edge-coloring with at most d + 1 colors. Furthermore, as it was earlier shown by K˝ onig, d colors suffice if the graph is bipartite. We investigate the existence of measurable edge-colorings for graphings. A graphing is an analytic generalization of a bounded-degree graph(More)
We study " positive " graphs that have a nonnegative homomor-phism number into every edge-weighted graph (where the edgeweights may be negative). We conjecture that all positive graphs can be obtained by taking two copies of an arbitrary simple graph and gluing them together along an independent set of nodes. We prove the conjecture for various classes of(More)
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