Loading...

Harmonious coloring of trees with large maximum degree

Akbari, S ; Sharif University of Technology | 2012

179 Viewed
  1. Type of Document: Article
  2. DOI: 10.1016/j.disc.2012.02.009
  3. Publisher: 2012
  4. Abstract:
  5. A harmonious coloring of G is a proper vertex coloring of G such that every pair of colors appears on at most one pair of adjacent vertices. The harmonious chromatic number of G, h(G), is the minimum number of colors needed for a harmonious coloring of G. We show that if T is a forest of order n with maximum degree Δ(T)≥n+23, then h(T) = {Δ(T)+2,if T has non-adjacent vertices of degree Δ(T);Δ(T)+1,otherwise.Moreover, the proof yields a polynomial-time algorithm for an optimal harmonious coloring of such a forest
  6. Keywords:
  7. Harmonious coloring ; Tree
  8. Source: Discrete Mathematics ; Volume 312, Issue 10 , 2012 , Pages 1633-1637 ; 0012365X (ISSN)
  9. URL: http://www.sciencedirect.com/science/article/pii/S0012365X12000817