Homotopy types of box complexes |
| |
Authors: | Péter Csorba |
| |
Institution: | (1) Department of Mathematics and Computer Science, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands |
| |
Abstract: | In 14] Matoušek and Ziegler compared various topological lower bounds for the chromatic number. They proved that Lovász’s
original bound 9] can be restated as X(G) ≥ ind(B(G)) + 2. Sarkaria’s bound 15] can be formulated as X(G) ≥ ind(B0(G)) + 1. It is known that these lower bounds are close to each other, namely the difference between them is at most 1. In this
paper we study these lower bounds, and the homotopy types of box complexes. The most interesting result is that up to ℤ2-homotopy the box complex B(G) can be any ℤ2-space. This together with topological constructions allows us to construct graphs showing that the mentioned two bounds are
different. Some of the results were announced in 14].
Supported by the joint Berlin/Zürich graduate program Combinatorics, Geometry, and Computation, financed by ETH Zürich and
the German Science Foundation (DFG). |
| |
Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 05C10 05C15 55P10 |
本文献已被 SpringerLink 等数据库收录! |
|