On a conjecture of Graham and Häggkvist with the polynomial method

  • Cámara M
  • Lladó A
  • Moragas J
  • 4

    Readers

    Mendeley users who have this article in their library.
  • 7

    Citations

    Citations of this article.

Abstract

A conjecture of Graham and Häggkvist states that every tree with m edges decomposes every 2 m-regular graph and every bipartite m-regular graph. Let T be a tree with a prime number p of edges. We show that if the growth ratio of T at some vertex v0satisfies ρ (T, v0) ≥ φ{symbol}1 / 2, where φ{symbol} = frac(1 + sqrt(5), 2) is the golden ratio, then T decomposes K2 p, 2 p. We also prove that if T has at least p / 3 leaves then it decomposes K2 p, 2 p. This improves previous results by Häggkvist and by Lladó and López. The results follow from an application of Alon's Combinatorial Nullstellensatz to obtain bigraceful labelings. © 2009 Elsevier Ltd. All rights reserved.

Get free article suggestions today

Mendeley saves you time finding and organizing research

Sign up here
Already have an account ?Sign in

Find this document

Authors

  • M. Cámara

  • A. Lladó

  • J. Moragas

Cite this document

Choose a citation style from the tabs below

Save time finding and organizing research with Mendeley

Sign up for free