Vertex-Colouring Edge-Weightings.
A weighting w of the edges of a graph G induces a colouring of the vertices of G where the colour of vertex v, denoted cv , is Σe∋vw(e). We show that the edges of every graph that does not contain a component isomorphic to K 2 can be weighted from the set {1, . . . ,30} such that in the resulting ve...
| Main Authors: | , , , , |
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| Format: | Journal article |
| Language: | English |
| Published: |
2007
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| Summary: | A weighting w of the edges of a graph G induces a colouring of the vertices of G where the colour of vertex v, denoted cv , is Σe∋vw(e). We show that the edges of every graph that does not contain a component isomorphic to K 2 can be weighted from the set {1, . . . ,30} such that in the resulting vertex-colouring of G, for every edge (u,v) of G, cu≠cv . © 2007 Springer-Verlag Berlin Heidelberg. |
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