Minimum H-decompositions of graphs: Edge-critical case


Ozkahya L. , Person Y.

JOURNAL OF COMBINATORIAL THEORY SERIES B, cilt.102, ss.715-725, 2012 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 102 Konu: 3
  • Basım Tarihi: 2012
  • Doi Numarası: 10.1016/j.jctb.2011.10.004
  • Dergi Adı: JOURNAL OF COMBINATORIAL THEORY SERIES B
  • Sayfa Sayıları: ss.715-725

Özet

For a given graph H let phi(H)(n) be the maximum number of parts that are needed to partition the edge set of any graph on n vertices such that every member of the partition is either a single edge or it is isomorphic to H. Pikhurko and Sousa conjectured that phi(H)(n) = ex(n, H) for chi (H) >= 3 and all sufficiently large n, where ex(n, H) denotes the maximum size of a graph on n vertices not containing H as a subgraph. In this article, their conjecture is verified for all edge-critical graphs. Furthermore, it is shown that the graphs maximizing phi(H) (n) are (chi(H) - 1)-partite Turan graphs. (C) 2011 Elsevier Inc. All rights reserved.