520 research outputs found
Asymmetric -colorings of graphs
We show that the edges of every 3-connected planar graph except can be
colored with two colors in such a way that the graph has no color preserving
automorphisms. Also, we characterize all graphs which have the property that
their edges can be -colored so that no matter how the graph is embedded in
any orientable surface, there is no homeomorphism of the surface which induces
a non-trivial color preserving automorphism of the graph
Color-blind index in graphs of very low degree
Let be an edge-coloring of a graph , not necessarily
proper. For each vertex , let , where is
the number of edges incident to with color . Reorder for
every in in nonincreasing order to obtain , the color-blind
partition of . When induces a proper vertex coloring, that is,
for every edge in , we say that is color-blind
distinguishing. The minimum for which there exists a color-blind
distinguishing edge coloring is the color-blind index of ,
denoted . We demonstrate that determining the
color-blind index is more subtle than previously thought. In particular,
determining if is NP-complete. We also connect
the color-blind index of a regular bipartite graph to 2-colorable regular
hypergraphs and characterize when is finite for a class
of 3-regular graphs.Comment: 10 pages, 3 figures, and a 4 page appendi
- …