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Vertex-coloring 2-edge-weighting of graphs
2011
European journal of combinatorics (Print)
A k-edge-weighting w of a graph G is an assignment of an integer weight, w(e) ∈ {1, . . . , k}, to each edge e. An edge weighting naturally induces a vertex coloring c by defining Given a graph G and a vertex coloring c 0 , does there exist an edge-weighting such that the induced vertex coloring is c 0 ? We investigate this problem by considering edge-weightings defined on an abelian group. It was proved that every 3-colorable graph admits a vertexcoloring 3-edge-weighting (Karoński et al.
doi:10.1016/j.ejc.2010.08.002
fatcat:leeebtfio5a5riearhouwom6wu