Loading...

Multicolored spanning subgraphs in G-colorings of complete graphs

Akbari, S

178 Viewed
  1. Type of Document: Article
  2. Abstract:
  3. Let G = {g1,...,gn} be a finite abelian group. Consider the complete graph with the vertex set {g1.....,.....g n}. The G-coloring of Kn is a proper edge coloring in which the color of edge {gi,gj} gi g i + gj, 1 ≤ i < 3 ≤ n. We prove that in the G-coloring of the complete graph Kn, there exists a multicolored Hamilton path if G is not an elementary abelian 2-group. Furthermore, we show that if n is odd, then the G-coloring of Kn can be decomposed into multicolored 2-factors and there are exactly lr/2 multicolored r-uniform 2-factors in this decomposition where lr is the number of elements of order r in G, 3 ≤ r ≤ n. This provides a generalization of a recent result due to Constantine which states: For any prime number p > 2, there exists a proper edge coloring of Kp which is decomposable into multicolored Hamilton cycles
  4. Keywords:
  5. Complete graph ; Harmonious ; Multicolored tree
  6. Source: Ars Combinatoria ; Volume 111 , 2013 , Pages 145-159 ; 03817032 (ISSN)
  7. URL: https://inis.iaea.org/search/search.aspx?orig_q=RN:39090578