Grad and classes with bounded expansion I. decompositions
组合数学
2007-05-23 v1
摘要
We introduce classes of graphs with bounded expansion as a generalization of both proper minor closed classes and degree bounded classes. Such classes are based on a new invariant, the greatest reduced average density (grad) of G with rank r, grad r(G). For these classes we prove the existence of several partition results such as the existence of low tree-width and low tree-depth colorings. This generalizes and simplifies several earlier results (obtained for minor closed classes).
引用
@article{arxiv.math/0508323,
title = {Grad and classes with bounded expansion I. decompositions},
author = {Jaroslav Nesetril and Patrice Ossona De Mendez},
journal= {arXiv preprint arXiv:math/0508323},
year = {2007}
}