Highly Influenced

10 Excerpts

@article{Akbari2011ColorfulPI, title={Colorful Paths in Vertex Coloring of Graphs}, author={Saieed Akbari and Vahid Liaghat and Afshin Nikzad}, journal={Ars Comb.}, year={2011}, volume={124}, pages={439-447} }

- Published in Electr. J. Comb. 2011

A colorful path in a graph G is a path with χ(G) vertices whose colors are different. A v-colorful path is such a path, starting from v. Let G 6= C7 be a connected graph with maximum degree ∆(G). We show that there exists a (∆(G)+1)-coloring of G with a v-colorful path for every v ∈ V (G). We also prove that this result is true if one replaces (∆(G) + 1) colors with 2χ(G) colors. If χ(G) = ω(G), then the result still holds for χ(G) colors. For every graph G, we show that there exists a χ(G… CONTINUE READING