Decomposition of sparse graphs into two forests, one having bounded maximum degree

  • Authors:

  • Mickael Montassier;André Raspaud;Xuding Zhu

  • Affiliations:

  • Université Bordeaux 1, LaBRI UMR CNRS 5800, France;Université Bordeaux 1, LaBRI UMR CNRS 5800, France;Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan and National Center for Theoretical Sciences, Taiwan

  • Venue:
  • Information Processing Letters
  • Year:
  • 2010

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Abstract

Let G be a graph. The maximum average degree of G, written Mad(G), is the largest average degree among the subgraphs of G. It was proved in Montassier et al. (2010) [11] that, for any integer k=0, every simple graph with maximum average degree less than m"k=4(k+1)(k+3)k^2+6k+6 admits an edge-partition into a forest and a subgraph with maximum degree at most k; furthermore, when k=