Lower bounds for the Crossing Number of the Cartesian Product of a Vertex-transitive Graph with a Cycle
نویسنده
چکیده
The minimum number of crossings for all drawings of a given graph G on a plane is called its crossing number, denoted cr(G). Exact crossing numbers are known only for a few families of graphs, and even the crossing number of a complete graph Km is not known for all m. Wenping et al. showed that cr(Km2Cn) > n · cr(Km+2) for n > 4 and m > 4. We adopt their method to find a lower bound for cr(G2Cn) where G is a vertex-transitive graph of degree at least 3. We also suggest some particular vertex-transitive graphs of interest, and give two corollaries that give lower bounds for cr(G2Cn) in terms of n, cr(G), the number of vertices of G, and the degree of G, which improve on Wenping et al.’s result.
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تاریخ انتشار 2014