An application of principal bundles to coloring of graphs and hypergraphs

Milgram, James R., and Zvengrowski, Peter. "An application of principal bundles to coloring of graphs and hypergraphs." Proceedings of the Winter School "Geometry and Physics". Palermo: Circolo Matematico di Palermo, 1994. [161]-167. <http://eudml.org/doc/221367>.

@inProceedings{Milgram1994,
abstract = {An interesting connection between the chromatic number of a graph $G$ and the connectivity of an associated simplicial complex $N(G)$, its “neighborhood complex”, was found by Lovász in 1978 (cf. L. Lovász [J. Comb. Theory, Ser. A 25, 319-324 (1978; Zbl 0418.05028)]). In 1986 a generalization to the chromatic number of a $k$-uniform hypergraph $H$, for $k$ an odd prime, using an associated simplicial complex $C(H)$, was found ([N. Alon, P. Frankl and L. Lovász, Trans. Am. Math. Soc. 298, 359-370 (1986; Zbl 0605.05033)], Prop. 2.1). It was already noted in the above mentioned papers that there is an action of $Z/2$ on $N(G)$, and of $Z/k$ on $C(H)$, for any graph $G$ and any $k$-uniform hypergraph $H$, $k \ge 2$ (a 2-uniform hypergraph is just a graph). In this note we take advantage of this action to construct an associated principal $(Z/k)$-bundle $\xi $, and state theorems relating the chromatic number of the graph or hypergraph to!},
author = {Milgram, James R., Zvengrowski, Peter},
booktitle = {Proceedings of the Winter School "Geometry and Physics"},
keywords = {Proceedings; Winter School; Zdíkov (Czech Republic); Geometry; Physics},
location = {Palermo},
pages = {[161]-167},
publisher = {Circolo Matematico di Palermo},
title = {An application of principal bundles to coloring of graphs and hypergraphs},
url = {http://eudml.org/doc/221367},
year = {1994},
}

TY - CLSWK
AU - Milgram, James R.
AU - Zvengrowski, Peter
TI - An application of principal bundles to coloring of graphs and hypergraphs
T2 - Proceedings of the Winter School "Geometry and Physics"
PY - 1994
CY - Palermo
PB - Circolo Matematico di Palermo
SP - [161]
EP - 167
AB - An interesting connection between the chromatic number of a graph $G$ and the connectivity of an associated simplicial complex $N(G)$, its “neighborhood complex”, was found by Lovász in 1978 (cf. L. Lovász [J. Comb. Theory, Ser. A 25, 319-324 (1978; Zbl 0418.05028)]). In 1986 a generalization to the chromatic number of a $k$-uniform hypergraph $H$, for $k$ an odd prime, using an associated simplicial complex $C(H)$, was found ([N. Alon, P. Frankl and L. Lovász, Trans. Am. Math. Soc. 298, 359-370 (1986; Zbl 0605.05033)], Prop. 2.1). It was already noted in the above mentioned papers that there is an action of $Z/2$ on $N(G)$, and of $Z/k$ on $C(H)$, for any graph $G$ and any $k$-uniform hypergraph $H$, $k \ge 2$ (a 2-uniform hypergraph is just a graph). In this note we take advantage of this action to construct an associated principal $(Z/k)$-bundle $\xi $, and state theorems relating the chromatic number of the graph or hypergraph to!
KW - Proceedings; Winter School; Zdíkov (Czech Republic); Geometry; Physics
UR - http://eudml.org/doc/221367
ER -