Combinatorial algebraic topology is a fascinating and dynamic field at the crossroads of
algebraic topology and discrete mathematics. This volume is the first comprehensive …

The local chromatic number of a graph was introduced in [14]. It is in between the chromatic
and fractional chromatic numbers. This motivates the study of the local chromatic number of …

The approximate graph coloring problem, whose complexity is unresolved in most cases,
concerns finding a-coloring of a graph that is promised to be-colorable, where. This problem …

First we prove that certain complexes on directed acyclic graphs are shellable. Then we
study independence complexes. Two theorems used for breaking and gluing such …

We prove several versions of Alon's necklace-splitting theorem, subject to additional
constraints, as illustrated by the following results.(1) The “almost equicardinal necklace …

We consider a natural graph operation Ω k that is a certain inverse (formally: the right
adjoint) to taking the k-th power of a graph. We show that it preserves the topology (the Z 2 …

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))+ …

Let G be an infinite graph such that the automorphism group of G contains a subgroup K≅ ℤ
d with the property that G/K is finite. We examine the homology of the independence …

The notion of×-homotopy from [Anton Dochtermann, Hom complexes and homotopy theory
in the category of graphs, European J. Combin., in press] is investigated in the context of the …

In this paper we provide concrete combinatorial formal deformation algorithms, namely
sequences of elementary collapses and expansions, which relate various previously …