Perfect packings with complete graphs minus an edge
组合数学
2007-05-23 v1
摘要
Let K_r^- denote the graph obtained from K_r by deleting one edge. We show that for every integer r\ge 4 there exists an integer n_0=n_0(r) such that every graph G whose order n\ge n_0 is divisible by r and whose minimum degree is at least (1-1/chi_{cr}(K_r^-))n contains a perfect K_r^- packing, i.e. a collection of disjoint copies of K_r^- which covers all vertices of G. Here chi_{cr}(K_r^-)=r(r-2)/(r-1) is the critical chromatic number of K_r^-. The bound on the minimum degree is best possible and confirms a conjecture of Kawarabayashi for large n.
引用
@article{arxiv.math/0605189,
title = {Perfect packings with complete graphs minus an edge},
author = {Oliver Cooley and Daniela Kühn and Deryk Osthus},
journal= {arXiv preprint arXiv:math/0605189},
year = {2007}
}