Colorful Paths in Vertex Coloring of Graphs

  title={Colorful Paths in Vertex Coloring of Graphs},
  author={Saieed Akbari and Vahid Liaghat and Afshin Nikzad},
  journal={Ars Comb.},
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

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