Homomorphism complexes andk-cores

Fold and Mycielskian on homomorphism complexes

Homomorphism complexes were introduced by Lovász to study topological obstructions to graph colorings. We show that folding in the second parameter of the homomorphism complex yields a homotopy equivalence. We study how the Mycielski construction changes the homotopy type of the homomorphism complex. We construct graphs showing that the topological bound obtained by odd cycles can be arbitraril...

Colourful Theorems and Indices of Homomorphism Complexes

We extend the colourful complete bipartite subgraph theorems of [G. Simonyi, G. Tardos, Local chromatic number, Ky Fan’s theorem, and circular colorings, Combinatorica 26 (2006), 587–626] and [G. Simonyi, G. Tardos, Colorful subgraphs of Kneser-like graphs, European J. Combin. 28 (2007), 2188–2200] to more general topological settings. We give examples showing that the hypotheses are indeed mor...

On Range Reporting , Ray Shooting andk - level

Analysis of Conserved Hydrophobic Cores in Proteins and Supramolecular Complexes

The conserved hydrophobic core is an important feature of a family of protein domains. We suggest a procedure for finding and the analysis of conserved hydrophobic cores. The procedure is based on using an original program called CluD (http://monkey.belozersky.msu.ru/CluD/cgi-bin/hftri.pl). Conserved hydrophobic cores of several families including homeodomains and interlock-containing domains a...

Rad51 and Dmc1 Form Mixed Complexes Associated with Mouse Meiotic Chromosome Cores and Synaptonemal Complexes

The eukaryotic RecA homologues RAD51 and DMC1 function in homology recognition and formation of joint-molecule recombination intermediates during yeast meiosis. The precise immunolocalization of these two proteins on the meiotic chromosomes of plants and animals has been complicated by their high degree of identity at the amino acid level. With antibodies that have been immunodepleted of cross-...