Vertex-coloring 2-edge-weighting of graphs

Hongliang Lu, Qinglin Yu, Cun-Quan Zhang
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.
more » ... ) [12]). Does every 2-colorable graph (i.e., bipartite graphs) admit a vertex-coloring 2edge-weighting? We obtain several simple sufficient conditions for graphs to be vertex-coloring 2-edge-weighting. In particular, we show that 3-connected bipartite graphs admit vertex-coloring 2edge-weighting.
doi:10.1016/j.ejc.2010.08.002 fatcat:leeebtfio5a5riearhouwom6wu