The purpose of this paper is to develop a homotopical algebra for graphs, relevant to the zeta series and the spectra
of finite graphs. More precisely, we define a Quillen model structure in a category of graphs (directed and possibly
infinite, with loops and multiple arcs allowed). The weak equivalences for this model structure are the Acyclics
(graph morphisms which preserve cycles). The cofibrations and fibrations for the model are determined from the
class of Whiskerings (graph morphisms produced by grafting trees). Our model structure seems to fit well with
the importance of acyclic directed graphs in many applications.
Publié le : 2009-05-15
Classification:
Category of directed graphs,
topos,
Quillen model structure,
weak factorization system,
cycles,
zeta function,
05C20,
18G55,
55U35
@article{1251832564,
author = {Bisson, Terrence and Tsemo, Aristide},
title = {A homotopical algebra of graphs related to zeta series},
journal = {Homology Homotopy Appl.},
volume = {11},
number = {1},
year = {2009},
pages = { 171-184},
language = {en},
url = {http://dml.mathdoc.fr/item/1251832564}
}
Bisson, Terrence; Tsemo, Aristide. A homotopical algebra of graphs related to zeta series. Homology Homotopy Appl., Tome 11 (2009) no. 1, pp. 171-184. http://gdmltest.u-ga.fr/item/1251832564/