An improved error term for minimum H-decompositions of graphs
Combinatorics
2011-09-13 v1
Abstract
We consider partitions of the edge set of a graph G into copies of a fixed graph H and single edges. Let \phi_H(n) denote the minimum number p such that any n-vertex G admits such a partition with at most p parts. We show that \phi_H(n)=ex(n,K_r)+\Theta(biex(n,H)) for \chi(H)>2, where biex(n,H) is the extremal number of the decomposition family of H. Since biex(n,H)=O(n^{2-\gamma}) for some \gamma>0 this improves on the bound \phi_H(n)=ex(n,H)+o(n^2) by Pikhurko and Sousa [J. Combin. Theory Ser. B 97 (2007), 1041-1055]. In addition it extends a result of \"Ozkahya and Person [J. Combin. Theory Ser. B, to appear].
Keywords
Cite
@article{arxiv.1109.2571,
title = {An improved error term for minimum H-decompositions of graphs},
author = {Peter Allen and Julia Böttcher and Yury Person},
journal= {arXiv preprint arXiv:1109.2571},
year = {2011}
}
Comments
9 pages