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

Hom (G, H) is a polyhedral complex defined for any two undirected graphs G and H. This
construction was introduced by Lovász to give lower bounds for chromatic numbers of …

To any two graphs G and H one can associate a cell complex Hom (G, H) by taking all graph
multihomomorphisms from G to H as cells. In this paper we prove the Lovász conjecture …

We investigate a notion of×-homotopy of graph maps that is based on the internal hom
associated to the categorical product in the category of graphs. It is shown that graph× …

Applied topology is a modern subject which emerged in recent years at a crossroads of
many methods, all of them topological in nature, which were used in a wide variety of …

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 show that the dominance complex D (G) of a graph G coincides with the combinatorial
Alexander dual of the neighborhood complex N (G‾) of the complement of G. Using this, we …

We show that the category of graphs has the structure of a 2-category with homotopy as the
2-cells. We then develop an explicit description of homotopies for finite graphs, in terms of …

Combinatorics, in particular graph theory, has a rich history of being a domain of successful
applications of tools from other areas of mathematics, including topological methods. Here …

The Hom complex $\mathrm {Hom}(G, H) $ of graphs is a simplicial complex associated to a
pair of graphs $ G $ and $ H $, and its homotopy type is of interest in the graph coloring …