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Colorful paths in vertex coloring of graphs

Akbari, S ; Sharif University of Technology | 2011

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  1. Type of Document: Article
  2. Publisher: 2011
  3. Abstract:
  4. 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 ≠ C7 be a connected graph with maximum degree Δ (G). We show that there exists a (Δ(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 (Δ (G) + 1) colors with 2 χ(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)-coloring of G with a rainbow path of length ⌊ χ(G)/2⌋ starting from each v ∈ V (G)
  5. Keywords:
  6. Colorful path ; Rainbow path ; Vertex-coloring
  7. Source: Electronic Journal of Combinatorics ; Volume 18, Issue 1 , 2011 , Pages 1-9 ; 10778926 (ISSN)
  8. URL: http://www.combinatorics.org/ojs/index.php/eljc/article/view/v18i1p17