Loading...

Multicolored trees in complete graphs

Akbari, S ; Sharif University of Technology | 2007

192 Viewed
  1. Type of Document: Article
  2. DOI: 10.1002/jgt.20204
  3. Publisher: Wiley-Liss Inc , 2007
  4. Abstract:
  5. A multicolored tree is a tree whose edges have different colors. Brualdi and Hollingsworth [5] proved in any proper edge coloring of the complete graph K2n(n > 2) with 2n -1 colors, there are two edge-disjoint multicolored spanning trees. In this paper we generalize this result showing that if (a1,..., ak) is a color distribution for the complete graph Kn, n ≥ 5, such that 2 ≤ a1 ≤ a2 ≤ ⋯ ≤ ak ≤ (n + 1)/2, then there exist two edge-disjoint multicolored spanning trees. Moreover, we prove that for any edge coloring of the complete graph Kn with the above distribution if T is a non-star multicolored spanning tree of Kn, then there exists a multicolored spanning tree T′ of Kn such that T and T′ are edge-disjoint. Also it is shown that if Kn, n ≥ 6, is edge colored with k colors and k ≥ (n-2 2) + 3, then there exist two edge-disjoint multicolored spanning trees. © 2006 Wiley Periodicals, Inc
  6. Keywords:
  7. Color ; Graph theory ; Probability distributions ; Complete graph ; Multicolored tree ; Rado's theorem ; Trees (mathematics)
  8. Source: Journal of Graph Theory ; Volume 54, Issue 3 , 2007 , Pages 221-232 ; 03649024 (ISSN)
  9. URL: https://onlinelibrary.wiley.com/doi/10.1002/jgt.20204