2 Eric Babson and Dmitry

Trends in Topological Combinatorics

I was the shadow of the waxwing slain By the false azure in the windowpane; I was the smudge of ashen fluff-and I Lived on, flew on, in the reflected sky. PREFACE This thesis is thought to be reflective of the transformation, mistily rendered in the citation on the previous page, which has taken place in me since I have handed in my Ph.D. thesis in the spring of 1996. If this transformation, no...

Cobounding Odd Cycle Colorings

We give a very short self-contained combinatorial proof of the Babson-Kozlov conjecture, by presenting a cochain whose coboundary is the desired power of the characteristic class.

Group Actions on Posets

In this paper we study quotients of posets by group actions. In order to define the quotient correctly we enlarge the considered class of categories from posets to loopfree categories: categories without nontrivial automorphisms and inverses. We view group actions as certain functors and define the quotients as colimits of these functors. The advantage of this definition over studying the quoti...

Topological Obstructions to Graph Colorings

For any two graphs G and H Lovász has defined a cell complex Hom (G,H) having in mind the general program that the algebraic invariants of these complexes should provide obstructions to graph colorings. Here we announce the proof of a conjecture of Lovász concerning these complexes with G a cycle of odd length. More specifically, we show that If Hom (C2r+1, G) is k-connected, then χ(G) ≥ k + 4....

Applications of Convex and Algebraic Geometry to Graphs and Polytopes